Chapter 20 Part 4 of My Life on the Plains. This LibriVox recording is in the public domain. I proceeded to the guard-fire which the three chiefs were still seated, engaged in conversation, and through Romeo inquired who the parties were whose voices we heard and their object. They informed me that the voices were those of some of their young men who were anxious to ascertain if their friends, the captives, were still alive, anxious that they should not only see that their friends were alive but well treated, I desired to induce them to come within our lines and visit the captive chiefs. This was communicated to them through the chiefs who called them in tones capable of being heard far beyond the point at which the young Indians were posted. But this did not satisfy their suspicious natures. They imagined some trap and decline to accept the invitation. Romeo, the only one who could converse freely in the Indian tongue, might have been able to persuade them to come in, but it was not safe for him to venture beyond the line of our pickets and trust himself in the power of the young Indians. In this emergency I thought of Manasita, in whom I had every confidence in who I believed might be successful in inducing her friends to come in. Sending for her I soon acquainted her with my plan to which she gave her ready assent, only expressing an apprehension that, in passing our own chain of sentries in the darkness, they might mistake her for an enemy and fire upon her. This difficulty I removed by offering to escorter safely through the line of pickets and there await her return. Starting at once in the darkness she, clinging to my hand with the natural timidity of a girl, we proceeded to the picket station nearest to the point from which the sound of the voices had come, and after explaining to the sentry our purpose passed beyond as far as it was prudent to do, and then bidding Manasita to proceed on her mission, I halted to await her return. A few moments later I heard her voice in the darkness calling to her friends beyond. Back came the quick respond, and soon I could distinguish the tones of the assembled group as Manasita endeavored to convince them of their security and trusting to the promises made to them. Arguments finally prevailed over their suspicions and in the dim light of the stars I could see her returning, accompanied by four or five others. Not caring to tempt them by meeting them alone so far from support, I slowly retired until I was near the picket post. Here the Indians found me, and after the form of an introduction by Manasita and a general hand shaking, the entire party proceeded without hesitation to the guard fire, where they joined their less fortunate chiefs. It may strike the reader with some surprise that Manasita herself, a captive in our hands, should have voluntarily returned to us that night, after once being safely beyond our lines. But she only confirmed the confidence that was placed in her. During her imprisonment, if her stay in our camp without a guard may be termed imprisonment, she had become a great favorite with the entire command. Not only this, but she believed she would in due time be given up to her own people, and that until then she would receive kind treatment at her hands and be exposed to less personal danger and suffering during hostilities than with her village. The visit of the young men to our camp that night could not but have had a beneficial influence upon the tribe as they weren't able to see that the three chiefs were being treated with the utmost consideration, and were being held as informed at first, simply as hostages to enforce compliance with demands, which even in Indian ideas of right and wrong must pronounce just. After a lengthy conversation between the captives and their friends, the latter took their departure, charged with messages to their village both from the captive chiefs and me, similar to those transmitted through the chief who had been released for that purpose. The following day was passed without incident in awaiting the arrival of tidings from the village. Early in the afternoon the pickets reported a small body of Indians in sight. Upon a nearer approach the party appeared to consist of about fifty mounted Indians. They rode steadily in the direction of the camp with no apparent wish to conceal their movements, thus indicating that they were on an errand of peace. When within a half a mile or less of camp the entire party dismounted, and after picketing their ponies out to graze, advanced on foot directly toward the camp. So strange a proceeding at a time when the excitement regarding our relations with the Indians ran high, was sufficient to assemble nearly all the occupants of camp to watch the approach of this delegation of Indians. The latter were apperelled in their best and most highly colored clothes. As they came near it was perceived that several paces in advance of the main group strode two chiefs, evidently leaders of the party, both advanced with uncovered heads. Suddenly I thought I detected a familiar face and form in the taller of the two chiefs in front, and on more careful scrutiny I recognized my former friend and guest, Little Robe, who had thus quickly responded to my invitation to cast aside all doubts and come and visit me, with a view to bringing about more friendly relations between his people and the whites. As soon as I recognized him I advanced to meet him. He grasped my hand and embraced me with what seemed to be real cordiality, waiting until the other members of his party came up. I shook hands with each individual, and then invited them to my tent. As the tent would not accommodate the entire party, Little Robe designated about a dozen of the most important who entered while the others remained outside. I soon found that in Little Robe I had a hearty co-agitor in the work before me. He admitted that the white girls were held as captives in the Cheyenne village, which was the first positive evidence received of this fact. He also stated, what I had no reason to doubt, that he had at various times attempted to purchase them, with a view, if successful, of returning them to the nearest military post. But as efforts in this direction had always failed. He admitted the justice of my demands upon his people, and assured me that to bring about a satisfactory condition of affairs he would use every exertion and employ all of the influence at his command. It was to assure me of this desire on his part that he had hastened to visit me. Knowing that the surest and speediest way to establish a state of good feeling and in Indian is to provide liberally for the wants of his stomach, I ordered a beef to be killed and distributed among the followers of Little Robe. With this also were distributed the usual supplies of coffee, sugar, flour, etc., so that their recipients were not only prepared to regard us as at least very kindly disposed, but I knew the effect on the village when the result of the visit and the treatment extended to our guests was described would materially aid us in our negotiations with the tribe. Little Robe, while earnest in his desire to see the white girls return to us, frankly admitted that his influence was not supreme, and there were those who would object to their release, at least without compensation, and it might be that a satisfactory settlement of the question might be delayed for many days. After partaking in a bountiful repast, Little Robe men his party set out for the village, prompting to send me word the following day as to his success. Another day was passed in waiting when the chief who had accompanied Little Robe the previous day again visited us, but brought no decisive or satisfactory reply. The substance of the reply was that the Cheyenne desired us to release the three chiefs, then held by us as hostages, after which they would be prepared to consider the question of the release of the two white girls. To this I sent back a reply that we would remain in the camp we then occupied until the following day, when, if a favorable answer should not be received, we would follow on their trail and encamp nearer to the village, the great distance and separating us about twelve miles, being a hindrance in the way of transmitting messages promptly from one to the other. I knew that the village was in no condition for a rapid or extended flight, and could be overhauled by the cavalry whenever desired. At the same time to allow as much freedom to their deliberation, says, possible. I had not been unwilling that a few miles should separate us. No reply was received. Consequently we packed up and marched down the sweet water on their trail of the village about ten miles and went into camp. Here I received another visit from the chief who had previously acted as diplomatic courier between the camp and village, but the response of the Cheyennes was still unsatisfactory and exhibited a disinclination on their part to make any decided promises respecting the release of the captive white girls. They insisted as preliminary to such decision that the three chiefs held by us should be restored to liberty, after which we might discuss the question relating to the release of the girls. I will not weary the reader by describing the various subterfuges resorted to by the Indians by which they strove to avoid or delay the surrender of the white girls without first, as has been customary, receiving a ransom. Finally, after I had almost exhausted the patience of the troops, particularly of the Kansas Regiment which had been raised and organized mainly to effect the recapture of the white girls, or also veng the outrage of which they had been the victims, I determined to force matters to an issue without further quibbling on the part of the Indians. I sent for a delegation of chiefs from the Cheyennes village to receive my ultimatum. They came and upon their arrival I assembled them in my tent. The three captive chiefs being also permitted to be present as the conference as will be seen was to be of deep interest to them. After recounting to the chiefs the incidence of our pursuit of the village, their surprise at being overtaken, the stratagems by which they hoped to elude us, the steps which we had already taken to obtain the release of the white girls and the delays imposed by the Indians, I stated that I had but one other message to be sent to the village, and upon the chiefs of the latter would rest the responsibility of the peace or war. Further delay would not be submitted to on our part. We knew they had two of our race captives in the village, and we were there to demand and enforce the demand for their release, cost what it might. I then informed them that if by sunset the following day the two white girls were not restored to our hands unharmed, the lives of the three chiefs would be forfeited, and the troops would resume active hostilities. At the same time I called attention to the fact that in the famished condition of their ponies they could not expect to escape the pursuit of the cavalry. Every argument which might have weighed in influencing a favorable decision was stated to them. The conference then broke up and the three chiefs were remanded to the custody of the guard. The delegation from the village after a brief interview with their captive comrades took a hasty departure and set out upon their return to the village, deeply impressed apparently with the importance of promptness and communicating to the chiefs at the village the decision which had been arrived at regarding the captives. The terms given to the Indians soon became known to every individual in the command and naturally excited the deepest interest. All hoped for a favorable issue, but no one regarded the events then transpiring with intense interest and anxiety felt by young Brewster, who now saw that his long cherished hope to recover his sister was either about to be realized or forever sealed in disappointment. The captive chiefs did not pretend to conceal their solicitude as to the part they were involuntarily made to play in the events then transpiring. I did not expect prompt action on the part of the chiefs in the village. I knew they would practice every delay conceivable before complying with our demands, but when the question was forced upon them as to whether they preferred to deliver up the white girls to us or to force by their refusal the execution of the three chiefs, their decision would be in favor of their people. Three o'clock arrived and no tidings from the village. By this time the officers and men of the command had assembled near headquarters and upon the small eminences nearby, eagerly watching the horizon in the direction of the village to catch the first glimpse of the messengers who must soon arrive to avert the execution of the three chiefs. Even the three chiefs became despondent as the sun slowly but surely approached the horizon with no tidings from the village reaching them. Finally Romeo came to me and stated that one of the three chiefs desired to see me. I repaired to their place of confinement at once and was asked by the younger the three if it was my firm purpose to make good my words in the event of the failure of their people to release the white girls. I replied in the affirmative. The chief then attempted a little Indian diplomacy by assuring me that in the village and among his own people he was a man of great consequence and could exert a wide influence. For this reason he requested me to release him and would hasten to the village, obtain the release of the two girls, and return in time to save his two companions. When this proposition was first made I attributed it to the fear that the chiefs in the village might decline to restore the two girls to liberty, and the lives of the three chiefs would be sacrificed thereby, but subsequent events proved that while this consideration may have had its influence, which prompted the proposition was a desire to escape from our hands before the white girls should be restored to us, as the chief referred to had been a party to their capture and to the subsequent ill treatment they had received. I replied to his proposal that if he was such of an importance in his tribe as he claimed to be, he was the most proper person for me to retain possession of, as his people would be more likely to accede to my demands to save his life than that of a person of less consequence. The sun was perhaps an hour high when the dim outlines of about twenty mounted figures were discerned against the horizon on a hill high two or three miles to the west of us. Instantly all eyes were directed to the party, but the distance was too great to enable any of us to clearly define either the number of characters of the group, the eyes of the three chiefs perceptively brightened with hope. Securing my field-glass I carefully scanned the party on the hill. Every one about me waited an anxious suspense to the result of my examination. Gradually, under the magnifying powers of the glass, I was able to make out the figures in sight. I could only determine at first that the group was, as might be imagined, composed of Indians and began counting them audibly when I discovered two figures mounted on the same pony. As soon as this was announced, several of my companions at once exclaimed, Can they be the girls? I could detect nothing, however, in their appearance warranting such a conclusion, the dress apparently being the same as that of other individuals of the group. While endeavouring to make out something more definite in regards to the party, I saw the two figures descend from the pony and leaving the rest of the group advanced towards us on foot. All this I reported to the anxious bystanders who became now more than ever convinced that the two figures approaching must be the two girls. I began describing the appearance of the two as well as I could with the aid of the glass. One seems to have a short, heavy figure. The other is considerably taller and more slender. Young Brewster, who stood at my side, immediately responded, That last one must be my sister. She is quite tall. Let me go and meet them. This thing sighed his more than I can endure. But this I declined, fearing that should one of the two now approaching us prove to be a sister, seeing her in the forlorn condition in which she must be, might provoke young Brewster beyond control and induce him to attempt to obtain revenge in a manner not governed by either prudence or propriety. So I reluctantly declined to permit him to advance beyond our lines. But by this time the two figures had approached near enough to enable me clearly to determine that they were really of weight complexion, and undoubtedly the two girls whose release we were so impatiently waiting for. As the Kansas volunteers had left their homes in various occupations in civil life to accomplish, among other results, the release of the two girls who had been abducted from their frontier of their state, I deemed it appropriate that that regiment should be the first to welcome the two release captives to friends and freedom. Accordingly, the three senior officers of the regiment were designated to proceed beyond our lines and conduct the two girls to camp, a duty whose performance carried its pleasure with it. The three officers advanced to meet the two figures. I used the term figures as the address was that nondescript pattern which renders this term most appropriate. They had passed one-fourth of the distance, perhaps when young Brewster, whom I had detained at my side with difficulty, bound it away, and the next moment was running at full speed to greet his long-lost sister. Dashing past three officers he clasped in his arms the taller of the two girls. This told us all we had hoped for. We awaited their approach, and as they drew near to the little brook which flowed just beyond the point occupied by the group of officers around me, I stepped forward, and extending my hands to the two girls bade them a hearty welcome to liberty. In a moment officers and men were struggling about them upon all sides, eager to take them by the hand and testify the great joy felt at their deliverance from a life of captivity. Men whom I had seen face death without quailing found their eyes filled with tears unable to restrain the deep emotion produced by this joyful event. The appearance of the two girls was sufficient to excite our deepest sympathy. Ms. White, the younger the two, though not beautiful, possessed a most interesting face. Her companion would have been pronounced beautiful by the most critical judge being of such a type as one might imagine Maude Müller to be. Their joy at the deliverance, however, could not hide the evidences of privation and suffering to which they had been subjected by their cruel captors. They were clothed in dresses made from flower sacks, the brand of the mills being plainly seen on each dress, showing that the Indians, who had held them in captivity, had obtained their provisions from the government at some agency. The entire dress of the two girls was as nearly like the Indian mode as possible. Both were leggings and moccasins. Both were their hair in two long braids as if to propotate us. The Indians before releasing them had added to the wardrobe of the two various rude ornaments such as are worn by squads. About their wrists they wore coils of brass wire, and their fingers had been placed numerous rings and about their necks strings of variously colored beads. Among the first remark I heard young Brewster make after the arrival of the two girls was, Sister, take those hateful things off. Fortunately they were not the only white women in camp.  They were conducted to the tent to the white woman referred to, from whose limited wardrobe they were able to obtain enough to replace the dresses made of flower sacks, and in a few minutes reappeared presenting a much more civilized appearance than when they first entered camp. In a previous chapter I have given the main incidents of their capture. The story of their captivity was that of a hundred other women and girls whose husbands, fathers or brothers, take their lives in their hands and seek homes on the frontier. There was much in their story not appropriate for these pages. They described how great their joy was at encountering each other from the first time as prisoners and hands of the Indians. They had been traded repeatedly from the hands of one chief to those of another, the last transfer having benefacted only two weeks prior to their release. Soon after their first meeting it was their good fortune comparatively to become the property of one chief. This threw them into each other's society and tended to lighten the whores of their captivity. While thrown together in this manner they planned an escape. Their planned seems was more the result of desperation than of careful deliberation as they had no ideas to what state or territory the village was then in, nor in what direction to travel should they escape from the village. Indeed one of their first questions on entering our line was to ask in what part of the country we were in. Determining all hazards, however, to flee from their captives as the first opportunity and trust a chance to lead them to the settlements or to some military post, they escaped from the village one night and traveled for several hours in a northerly direction. During this attempt to regain their liberty they reached a wagon road over which wagons and horses had passed recently and were congratulating themselves upon the success of their effort when a bullet whistled past them and in close proximity to them. Casting an anxious look they sought to their horror and disappointment their late captor or owner riding at full speed in pursuit. Escape was impossible. Nothing remained but to await the arrival of the chief who came up excited and in savage rage at the idea of their attempt to escape him. Marching back on foot to the village they became the recipients of renewed insults and taunts, nor did it end there. The squads of the village always jealous of white women when captives took this opportunity to treat them with the greatest severity for their attempt to regain their liberty. The old chief also decided upon a change of program. He had invested several ponies when he had become the possessor of the two girls and he did not propose to risk the loss of this property, so he determined to separate the two girls by selling one of them and the two friends in misfortune were torn from each other. Miss White, in consideration of the three ponies given an exchange, passed into the hands of another chief whose lodge was generally located some miles from that of her late master. The story of the two girls containing accounts of wrongs and ill-treatment sufficient to have ended their existence of less determined persons is too long to be given here. Besides indignities and insults far more terrible than the death itself, the physical suffering to which the two girls were subjected was too great almost to be believed.  They were limited to barely enough food to sustain life. Sometimes a small morsel of mule meat, not more than an inch square, was their allowance of food for twenty-four hours. The squads beat upon them unmercifully with clubs whenever the men were not present. Upon one occasion one of the girls was felt to the ground by a blow from a club in the hands of one of the squads. Their joy therefore at regaining their freedom after the captivity of nearly a year can be better imagined than described, while that of the brother who had struggled so long and determinately to regain his sister could not be expressed in words. After the momentary excitement consequent upon the safe arrival of the girls in camp had subsided, officers particularly of the Kansas volunteers came to me with remark that when we first overtook the Cheyenne village and I failed to order an attack, when all the chances were in our favor, they mentally condemned my decision as a mistake. But with the results accomplished afterwards they found ample reason to amend their first judgment, and frankly and cordially admit that the release of the two captives was far more gratifying than any victory over the Indians could have been purchased by the sacrifice of their lives. With this happy termination of this much of our negotiations with the Indians, I determined a march in the mourning for camp supply, Indian territory, satisfied that with the three chiefs in our possession and the squads and children captured at the Washtaw, still held as prisoners at Fort Hays, Kansas, we could compel the Cheyennes to abandon the warpath and return to their reservation. The three chiefs begged to be released upon the grounds that their people had delivered up the two girls, but this I told them was but one of the two conditions imposed. The other required the tribe to return to their reservation, and until this was done they need not hope for freedom, but in the meanwhile I assured them of kind treatment at our hands. Before dark a delegation of chiefs from the village visited the camp to likewise urge the release of the three chiefs. My reply to them was the same as that I had given to the captives. I assured them, however, that upon complying with their treaty obligations and returning to their reservation, the three chiefs would be restored to their people and we would return to them, also the women and children captured at the Washtaw. Seeing that no modification of these terms could be obtained, they finally promised to accede to them, saying that their ponies, as I knew to be the fact, were in no condition to travel. But as soon as practicable they would surely proceed with their entire village to camp supply and abandon the war-path forever, a promise which as a tribe they have adhered to, from that date of this with strict faith, so far as my knowledge extends. I had not heard from General Sheridan since we separated at Fort Sell. He too set out for camp supply and I with my command to begin my present movement. But when near camp supply a courier met me with dispatches from General Sheridan, who had been meanwhile summoned to Washington, informing me in regard to the arrangements made for my command upon its arrival at camp supply. The Kansas volunteers were to march to Fort Hayes and there be mustered out of service. The Seventh Cavalry was also to proceed to the same point and their await further orders, as the General in his notes stated, that he had concluded to draw in the Seventh and end the campaign. In reply to my letters written subsequently from camp supply, giving him a detailed account of our operations, including the release of the two white girls, I received a letter of warm encouragement from the General written from Chicago, where he had just established his present headquarters. In that letter he wrote, I am very much rejoiced at the success of your expedition and feel proud of our winter's operation and of the officers and men who have borne its privations and hardships so manfully. Give my kind regards to the officers and say how happy I should be to see them should any of them come this way and leave. These words of hearty sympathy and approval from one who had not only shared but appreciated at their true worth are privations and hardships were far more cheering and valued than the empty honor contained in a half a dozen brevets bestowed grudgingly and recalled in a moment of peak. Making a brief halt at camp supply to rest our animals and replenish our stores, my command continued its march to Fort Hayes crossing the Arkansas River at Fort Dodge, Kansas. Upon our arrival at Fort Hayes we were met by the husband of the young Brewster's sister, who had learned of her restoration to liberty from the published dispatches which had preceded us to Fort Hayes.  The joy of their meeting went far to smooth over their late sorrow. They could not find languages to express their gratitude to the troops for their efforts in restoring them to each other. As the Indians had robbed them of everything at the time of the attack, a collection was taken up among the troops for their benefit which resulted in the accumulation of several hundred dollars to be divided between the two captives. The time came for our guests to leave us and rejoin their people or such of them as had survived the attack of the Indians. Goodbyes were spoken and the two girls so lately victims of the most heartless and cruel captivity departed with husband, brother, and friends for their frontier homes, bearing with them the warm sympathies and cordial good wishes of every soldier in the command. Manasita was anxious to visit her friends who were now captives at Fort Hayes and who were kept in a large stockade at the post, our camp being placed some two or three miles below the post. Accordingly she repaired to the stockade and spent several hours relating no doubt the story of our march since they had separated from each other. She preferred to live in the cavalry camp when she was allowed to roam without the restraint of a guard, but it was deemed advisable soon after to place her with the other women and children inside the stockade. The three captive chiefs were also transferred to the same place for safekeeping. Here a most unfortunate misunderstanding arose. The chiefs had been confined inside the same enclosure with the women and children, but in separate tents. The commanding officer of the post decided to remove them to rooms in the guard house adjoining the stockade. This was decided upon as a measure of security. There was no interpreter kept at the post. Consequently there was no way of communicating with the Indians except by rude signs and even this method was but indifferently understood by the infantry soldiers constituting the garrison of the post. From accounts given to me by the Indians afterwards, it seems the man of the guard in the execution of the order to transfer the three chiefs entered the stockade muskets in hand and upon the failure of the chiefs to comprehend what was required of them, soldiers attempted to push the chiefs from the stockade by force, pointing with their bayonets to the outside. The chiefs failing to understand a word spoken to them and with the natural suspicion of their race, imagined that they were being led or driven forth to execution and determined to die there and then. An attack was at once made upon the guard with knives which they had carried beneath their blankets. The sergeant of the guard received a stab in the back which almost proved mortal. This was a signal for a determined fight between the three chiefs and the guard, the latter having the decided advantage in numbers and weapons. The result could not be long doubtful. One of the chiefs, Big Head, the young man who had proposed to proceed to the village to obtain the release of the two white girls, felt dead at the first fire of the guard. The oldest of the three dull knife received a bayonet wound through the body which proved fatal in a few days.  Knowing that I could converse with the Indians and from my acquaintance with them I'd be able to quiet the excitement among the remaining prisoners, the commanding officer the post sent for me for assistance. Upon repairing to the stockade I found the women and children in a state of great excitement and huddled together inside their tents. Entering the stockade I soon learned their version of the affair which did not vary materially from that just given. Monicita pointed to a bullet hole in her blanket, the effect of a stray shot fired during the melee. The affair was a source of deep regret to all. The Cheyennes, in accordance with their promises made to me, returned to their reservation and, having thus far complied with the terms of the agreement then made, it devolved upon the military authorities to return to them their people whom we had up to that time and since the Battle of the Washita retained as prisoners of war. An order was accordingly issued releasing the only surviving chief, fat bear, and the women and children that were held at Fort Hayes. Wagons and sub-stenents were furnished them from Fort Hayes to Camp Supply and a squadron of the Seventh Cavalry escorted them to the latter point where they were received by their own people. Monicita, although gladdened by the prospect of being restored to her people, exhibited mark feelings of regret when the time for her departure arrived. She had grown quite accustomed to the easy idle life she had led among the troops as compared with the mere existence of toil and drudgery to which all tribes of Indians consign their squads. Romeo, who had accompanied us throughout the events described in these pages as the interpreter, took on to himself a wife from the Cheyenne village and thereafter became a sort of traitor between the Whites and Indians. I believe he is still acting in that capacity. Lone Wolf is still the leading chief for the Kiowas, but if public and private advices are to be relied upon, he has acted with extremely bad faith toward the government, and even as these lines are being penned, is reported as absent from his reservation, leading a war-party of his people in committing depredations upon the people of the Texas Frontier. Satana, since his release from the Texas State Prison, has led a comparatively quiet and uneventful life. How much of this is due to his incarceration of prison for a short term of years, can only be inferred. Little Raven continues to exercise the powers of head chief of the Arapahos, although he is too old to infirm to exercise active command. My former friend and companion, Yellow Bear, is the second chief in rank to Little Raven, and probably will succeed to the dignities of the later heir many years have ruled around.  A few words in regard to one other character with whom the reader of these sketches has been made acquainted, and I shall have disposed of the principal personages not included in the military, whom the reader has encountered from time to time. California Joe, accompanied my command to Fort Hayes, Kansas, on the Kansas Pacific Railroad, when the troops were partially disband and sent to different stations, California Joe had never seen a railroad nor locomotive, and here determined to improve his first opportunity in these respects and to take a trip in the cars to Leavenworth, distant about 400 miles. A few days afterward an officer of my command happened to be called to Leavenworth, thought he recognized a familiar form and face in front of the leading hotel of the city. A closer scrutiny showed that the party recognized was none other than California Joe. But how changed? Under the manipulations of the barber and through the aid of the proprietor of a gentleman's furnishing store, the long curly locks and beard of California Joe, both of which had avoided contact with comb, brush, or razor for many years, had undergone a complete metamorphous. His hair and beard were neatly trimmed and combed while his figure, a very commanding one, had discarded the rough shirt of the frontiersman, and had now adorned by the latest efforts of fashion. If the reader imagines, however, that these changes were in keeping with the taste of California Joe by impression, is wholly incorrect. He had affected them simply for a sensation. The following day he took the cars for the West satisfied with the faint glimpse of civilization he had had. As I soon after left that portion of the plains in which these scenes are laid, I saw no more of California Joe. But I often wondered what had become of my loquacious friend, whose droll sayings and quaint remarks had often served to relieve the tedium of the march and to enliven the group about the campfire. I had begun after a few years as passed without tracer tidings from Joe to fear that he had perhaps gone to the happy hunting ground to which he no doubt had sent more than one dusky enemy. When a few weeks ago I was most agreeably surprised to receive indubitable evidence that California Joe was still in the land of the living, but exactly where I could not determine. As his letter was simply dated, Sierra Nevada Mountains, California. Now, as this range of mountains extends through the entire length and embraces a considerable portion of the state of California, Joe's address could not be definitely determined. But as his letter is so characteristic of the man, I here introduce it as the valedictory of California Joe. Sierra Nevada Mountains, California. March 16, 1874. Dear General, after my respects to you and Lady, I thought that I tell you that I am still on top of land, yet I have been in the Rocky Mountains the most of the time since I last seen you. But I got on to railroad and started west, and the first thing I knew I landed in San Francisco, so I could not go any further except going by water and salt water at that. So I turned back and headed for the mountains once more resolved never to go railroad no more. I drifted up with the tide to Sacramento City and I landed my boat. So I took up through town and they say there's 20,000 people living there, but it looked to me more like 100,000, counting Chinaman and all I can't describe my wolfish feeling, but I think that I looked just like I did when we was chasing Buffalo on the Cimarron. So I struck up through town, and I come to a large fine building crowded with people, so I bulged in to see what was going on, and when I got into the council house I took a look around at the crowd, and I see the most of them had bald heads. So I thought to myself, I stuck it now that they are Indian peace commissioners. So I looked to see if I would knew any of them, but not one. So after a while the smartest looking one got up and said, gentlemen, I introduce a bill to have speckle mountain trout and fish eggs imported to California to be put in the American Bar and Yuba Rivers. Those rivers is so muddy that a tadpole could not live in them caused by mining. Did anybody ever hear of a speckle trout living in muddy water? And the next thing was the game lawn that was very near as bad as a fish, for there ain't no game in the country as big as Muck and Bird, and I heard some fellow behind me ask how long is the legislature spent in session. Then I dropped on myself it wasn't Indian commissioners after all. So I slid out and took across to Chinatown, and they smelled like a Kiowa camp in August with plenty buffalo meat around. It was getting late, so no place to go, not got a red scent. So I happened to think of an old friend back in town, and I'd known 25 years ago. So I lit out and sure enough he was there, just as I left him 25 years ago. Batchon! So I got a few seeds. I'd gone to plant in a few days, give my respects to the Seventh Cavalry, and accept the same yosely. California Joe. The events described in this chapter terminated my service in the field on what is known as the Southern and Middle Plains, embracing all that portion of the plain south of the Plant River. From and after the Washington Campaign, the frontiers of Kansas have enjoyed comparative peace and immunity from Indian depredations. No general Indian war has prevailed in that part of the country, nor is it probable that anything more serious in this way than occasional acts of horse-stealing will occur here after. Many of my friends have expressed surprise that I have not included in Life on the Plains some of the hunting scenes and adventures which had formed a part of my experience. But I feared the introduction of this new feature, although probably the pleasantest and in many respects the most interesting of my recollections of border life might prolong the series of articles far beyond the length originally assigned to them. I hope, however, at an early day to relate some of the experiences with the large game so abundant on the Plains, and in this way fill up the blank in these articles which my friends, who are lovers of the sport, have not failed to observe. As I pen these lines I am in the midst of scenes of bustle and busy preparation, attendant upon the organization and equipment of a large party for an important exploring expedition, on which I shall start before these pages reach the publisher's hands. During my absence I expect to visit a region of the country, as yet unseen by human eyes except those of the Indian, a country described by the latter as a bounding in game of all varieties, rich in scientific interest and of surpassing beauty and natural scenery. Bidding a due to civilization for the next few months, I also now take leave of my readers, who I trust in accompanying me through my retrospect, have been enabled to gain a true insight into a cavalryman's life on the Plains. The End. End of Chapter 20, Part 4. End of My Life on the Plains or Personal Experiences with Indians by George A. Custer. This has been a LibriVox recording. All LibriVox recordings are in the public domain. If you'd like more information or how to volunteer, please visit LibriVox.org.


I'm Ian Copeland, the principal of the Whodan School in the ACT. The Whodan School is a secondary school from year 7 to 12 for students with intellectual disability and autism. This school, while it's a specialist school, is really a high school like any other high school in the country. And we wanted to ensure that our students get the same opportunities and the same chances to study and understand the broader world and the Australian curriculum gave us that passage into that learning. What we obviously need to do, however, is adapt the Australian curriculum to meet the needs of all of our students. Our fundamental starting point is saying, let's look at the content that's relevant for them in the year level that they're at. So a year 9 student in history, in English, in science, have a look at the year 9 content there and see whether that's appropriate, relevant and accessible to those students. And if not, then make some decisions about how we might address that. We start with the 20-week plans. And the 20-week plans allow the teacher to have a clear understanding of how the semester is going to look like. Now, because all of our classrooms are streamed as well, according to ability. But even in each of those classrooms, there are different abilities for different students. So what we do, we use the general capabilities to differentiate the learning outcomes of each one of our students. So even though in our planning we can have up to 15-20 outcomes, we're only going to pick, for reporting, for assessment, only four of those outcomes. And those outcomes are going to be completely individualized for each one of our students in the classroom. Of course we have to make it relevant for our students and if it's not relevant, it's not significant and then it becomes just another thing that they heard somewhere. But when we make those connections and we work towards those connections, it's where our students actually, it's enriching for our students and they can then have adult conversations at home with their parents, with their friends. I remember teaching the Vikings in one of the semesters. And so the parent came and talked to me later on and says to me, oh, you know, I was so impressed because my son, we were watching this show and then suddenly he started talking about all this different content in the movie and where did they leave and what did they use to travel and the outfits they were wearing, what were they made of, the food that they were eating. So those are the kind of things that when they are learning here at school then they get transferred in a day-to-day situation in the living room with their parents and their families and I think that's kind of wonderful. We do plan in teams. Every class in the school is different, every individual student in the school is different so there's a lot of collaboration talking between teachers who teach the same student and the LSAs as well, all of our support staff that we're all very aware of what each child, where they're at, what they need to achieve to their potential. So if we're planning something we also like to collaborate in a way that keeps it consistent. The Australian curriculum is fully embedded in the way that this school operates and the effect of that has been that teachers are sure about what they can teach. They have a great resource to access, to develop their programs. Parents have a great understanding of what is being taught in classes because we send home the unit outlines with the outcomes all described and parents feel that their students are getting a real high school education.


But now how are you? How are you? Yeah, thanks for having us here today. I think the event's going very well. I like the story. It seems like you guys have really thought this one through. How long have you been with the company? I joined Mercury Interactive in 1998. So if you add up my cumulative experience, I've been doing this for roughly 15 years. I've got it finished such a long time. So take me through those 15 years and where we are today. 15 years ago, what was your job? What were you doing? It's interesting. I was in the field. I was responsible for building a pre-sales organization which serviced Mercury Interactive's quality of customers. So at the time, 15 years ago, everything was about automated testing. And it was automated testing at the GUI. And the big worry, and it's unfortunate for I-100, is whether or not their apps were going to survive the year 2000 switchover. So if you remember those days, millions and millions of dollars being funneled just to make sure these apps would stay alive because everyone thought their businesses would be out of business at the turn. That was driving Mercury's business in the early days. We transitioned very quickly, I should say, to the dot-com mania. In mid-1999, it was all about web development. Everybody was chasing each other. They were putting up their first corporate web pages and many circumstances. Literal story, I was called at dinner at 7 PM by the men CIO of Walmart.com. He's asked if my team could show up that night to do a 30,000 user load test because Walmart.com is going up the next day. And the CEO just heard about all the outages associated with websites that couldn't scale. And we were at Walmart.com all night doing a load test for these guys. It was crazy times. And now load testing has a whole different meaning. No, it totally does. You think about the complexity of the apps. These were simple websites. The most complicated thing was adding a widget to a cart processing a credit card. Now everything is composite apps and then there's the processing.


Ok so I will state and prove the cyclic decomposition theorem ok I have mentioned this before what the statement is I will make the precise statement a little later but I need to tell you what is the problem. The question is can we write a finite dimensional vector space V as follows Z X 1 T direct sum Z X 2 T etc Z X K T that is can I decompose a finite dimensional vector space V such that into a sum of you know into a direct sum of subspaces such that each subspace is cyclic cyclic with respect to the operator T. So can I find vectors X 1 X 2 etc X K such that this decomposition is possible ok the answer is yes it is related to the following problem this is related to the following problem. See this is the reason why one must look for such a decomposition is that dealing with operators over cyclic subspaces is easier than dealing with operators over the general space. So one would like to look at the restriction operators the restriction of the operator T on the cyclic subspace then we have already derived some consequences for example if you look at the matrix of the restriction of T over the subspace that is a companion matrix etc ok I have not mentioned that is a restriction operator but it is essentially that. So there are some simplifications possible when you study an operator T by restricting the operator to certain subspaces in this instance the cyclic subspaces this problem is related to another problem which is the following. Given a finite dimensional vector space V there are subspaces W and W prime such that V is a direct sum of these two subspaces now for a finite dimensional vector space this is true even though we will not prove it in this course this is true now what is possible is that given a subspace W of V which is not the whole of V in the finite dimensional case there are infinitely many choices for W prime given a subspace W there are examples where given a subspace W there are infinitely many choices of W prime ok I can give a simple example motivated by the geometry of R2 this gives a decomposition the horizontal axis the vertical axis this gives a decomposition take the horizontal axis and look at the subspace generated subspace of all points lying on this line passing through the origin horizontal space and this slanted space this subspace has the property that the sum is a direct sum decomposition of R2 you can verify this easily unit vector is 1 0 you can take this is the line Y equals X so unit vectors 1 by root 2 comma 1 by root 2 then any these two vectors are independent so these two vectors from a direct sum decomposition of R2 so in fact any line so take the horizontal and take any slanted line set of all points lying on that line that will be a subspace these two together will give rise to a direct sum decomposition of R2 this can be done in Rn also. So given a subspace it is possible that there are infinitely many subspaces W prime that satisfy this condition we call W prime as a subspace complementary to W W prime is called a complementary subspace is called a complementary subspace complementary to W complement to W it is called a complementary subspace complement to W the question is if you have an operator T can I also look for T invariant subspaces can we extend this to a problem where suppose I have suppose the T of W is contained in W that is W is invariant under T can I get a W prime such that W prime is also invariant under T does there exist W prime a subspace such that W prime is also invariant under T this is rather too much to expect the answer is in general no okay but we will give a condition under which this holds we will we can impose okay the general answer to this question is no general answer to this question is yes given a subspace W in a finite dimensional vector space given a subspace W can I find a complementary subspace W prime this is always possible given a subspace W such that given a subspace W that is invariant under T can I find a subspace W prime which is also invariant under T answer is no I will give an example so that you will be convinced to get an to get an affirmative answer you need to impose something more on W that is what I will discuss next but I will give an example to show that the answer in general is no look at look at the following operator T the matrix of T I will write okay I will write T straight away let us look at this diagonal matrix 1, 2, 0, 0, 0, 3 you look at the space which is nulls 2, 2, 3 are the eigenvalues look at null space of 2 minus T I call that W I am not going to show but I am going to leave this as an exercise show that this see this W is an eigen space so T W is contained in W this is invariant under T that is not a problem okay but there exists no W prime such that W plus W prime is R 3 together with the condition that T W prime contained in W prime okay so if you are seeking an invariant subspace if you are given an invariant subspace W if you are seeking an invariant subspace W prime the answer in general is no you need some more conditions on W so that this will be satisfied what is that condition that condition is called T admissibility that condition is called T admissibility so let me give this definition condition on a subspace being T admissibility so this is a framework V is a finite dimensional vector space T is an operator on V W is a subspace this subspace W is called T admissibility if the following two conditions are satisfied the first condition is that it must be invariant under T the second condition is that if F T of Y belongs to W where F is any polynomial if F T Y belongs to W then there exists Z in W such that F T Y equals F T Z for any polynomial F this is T admissibility okay where does this come from for one thing the questions how is this related to the notion that we discussed just now how is this related to seeking a subspace W prime which is also invariant under T given that there is a subspace W which is invariant under T with the assumption that W plus W prime is the whole space W comma W prime gives a direct sum decomposition where does it come from if I have a subspace W given a invariant subspace W so let me make the statement this is easy to see a little lemma maybe let V be W direct sum W prime with the following T W is contained on W T W prime is contained in W prime then W is T admissibility then W is T admissibility this is very easy to see the converse is not at all easy the converse is non-trivial the converse is non-trivial consequence of the cyclic decomposition theorem what is the converse is the question that I asked you to begin with okay how does this follow this is very easy let me prove this quickly I want to show that this condition is satisfied by W okay see this I want to show that W is T admissible okay these conditions do not involve W prime okay I want to show W is T admissibility so let me start with F T Y in okay I will start like this this is take an arbitrary vector in the vector space then I can write that as Y 1 plus Y 2 Y 1 is in W Y 2 is in W prime in a unique way because of the direct sum decomposition V is a direct sum decomposition so this representation is unique for any polynomial F I look at F T Y F T is linear so F T Y is F T Y 1 plus F T Y 2 both these subspaces are T invariant so this belongs to W this belongs to W prime because both these are invariant subspaces if this belongs to W if this belongs to W then what is the consequence this has to be 0. So F T Y belongs to W this statement will imply that F T Y 2 is 0 this is in W F T Y 2 is 0 if F T Y 2 is 0 it means F T Y is F T Y 1 that is F T Y equals F T Y 1 with the extra provision for us that Y 1 belongs to W this is the condition 2 this is the second condition if F T Y belongs to W then there must be exist Z such that F T Y equals F T Z in this case Z is Y 1 okay so this is a simple consequence of the fact that both W and W prime forming a direct sum decomposition of V are invariant under T okay the converse is not that easy it is a consequence of the cyclic decomposition theorem. So this is a notion that is relevant to the statement of the decomposition theorem T admissibility of a subspace so let me write on the statement T is a linear operator on a finite dimensional vector space V let W be a T admissible proper subspace of V W is a T admissible proper subspace of V so W is not the whole of V but W could be single term 0 T admissible proper subspace of V then what we want to show is that there exist non-zero vectors I will call them X 1 X 2 etc X R non-zero vectors in V such that the following conditions hold condition 1 is that V is the direct sum of I will start with W not W 0 is the invariant subspace T admissible subspace that I start with then V can be shown to be the direct sum of W not and these subspaces Z X 1 T X 2 T etc X Z X R T I also have another condition there exist T annihilators there exist T annihilators there exist T annihilators I will call them P K 1 less than or equal to K less than or equal to R T annihilators of what of the X K's T annihilators P K corresponding to the vector X K that is P K is a T annihilator of X K etc for 1 up to R K running from 1 up to R such that I have this condition P K divides P K minus 1 for all K K running from 2 to R this time this is P K divides P K minus 1 ok maybe I will just write P K divides P K minus 1 for K equal to 2, 3 etc R the last part says that last part I will write here itself further the integer R that is what is the number of vectors X 1 etc X R that integer R and P K the integer R and P K for which 1 and 2 hold for which 1 and 2 hold are unique ok that is the complete statement as I mentioned before this has 4 steps the last step is the uniqueness I am going to skip the last step uniqueness is not very important so I will skip the last step I will take the other 3 steps and prove this theorem ok you could ask this question how does this answer how does this decomposition answer the one that we started with Z X 1 P etc Z X R T I mentioned that you could start with W not to be singleton 0 so this will not be there so V is a direct sum of this is called the cyclic decomposition of the vector space V we also have extra things about the annihilators and how they are related ok ok there are 3 steps here as I mentioned the proof has 3 steps first step is to show the following step 1 we show that there exists vectors Y 1 Y 2 etc Y R in V there exist nonzero vectors there exist nonzero vectors such that such that V is not the direct sum it is just the sum W not plus Z Y 1 T etc Z Y R T ok note that this is not the direct sum just the sum this is the first condition second condition if W K is W not plus Z Y 1 T etc Z Y K T W K is the subspace I get by adding these K subspaces to W not that is W K if W K is this for 1 less than or equal to K less than or equal to R then the conductor then the conductor P K I will use S Y K W K minus 1 this is a notation I have got to explain this notation ok I will do it a little later P K is a polynomial it is a conductor this conductor has the following property has the maximum degree so I must tell you that the statement is complicated but the proof of this is easy first step has a maximum degree among all T annihilators into W K minus 1 what is the meaning of this see W K is this subspace I look at a particular polynomial this polynomial is denoted by P K this P K has a property that among all the T annihilators into W K minus 1 this one has a maximum degree so let me write down the formulation P K is P K is maximum over all maximum X element of V S of X comma W K minus 1 I have still not defined what this little S is I will do this now and then prove this first step once I define S the second part should be clear. So what is this S you recall this subspace S T X W for a subspace so this is really to recall this notion this is the T conductor of X into W that is the set of all polynomials G such that G T X belongs to W this is the T conductor of X into W this is S T we know that this is an ideal this is an ideal in the principal domain F D F D so this is generated by a unique monic polynomial that monic polynomial I will denote it by little S okay to be specific this S for me will be X comma W K minus 1 this is the this is generated by the polynomial S that unique monic generator S to denote that it depends on X and the subspace W sorry and the subspace W I will denote it like this S X W so little S always denotes the unique monic generator of a particular ideal of polynomials in this instance it is X W S T X W so it is determined by X and W okay so now go back and check this go back and see what what this definition is look at all see look at S X W K minus 1 I told you what this is you look at that ideal S T X comma W K minus 1 fix an X and then your little S X W K minus 1 is a unique monic generator of that ideal you vary X in V and take the maximum of the degree of all those okay then I must mention degree P K degree P K if P K see this is this is an infinite set okay X belongs to V I look at the maximum of the degrees of I must also write maximum degree here so please make this correction also maximum of the degrees of these polynomials the polynomial is S I look at the degrees of those and I will maximize that degree what I am saying is that maximum degree will be equal to degree of P K where what is P K P K is this particular polynomial P K is this particular T annihilator that is you look at the unique monic generator of the ideal capital S Y K W K minus 1 that is this little S if that is denoted by P K then P K has this maximum property okay so I look at this ideal take the unique monic generator I am calling that as P K what is the property that P K has with W K minus 1 what is the property that P K has with W K minus 1 in relation to W K minus 1 this is that property among all those vectors X which are taken for that for that ideal I compute those polynomial unique monic polynomials take the maximum of those degrees that degree that number will be equal to degree of this polynomial okay only those numbers coincide so proof of step 1 let us say I want to start with the invariance of space W not I want to start with the invariance of space W not and then construct this V I would rather start with an invariance of space W and then apply W not for that let W be an invariance of space of V that is T of W is W contained in W I take an arbitrary vector Y in V if W is a proper invariance of space of V then we have the following inequalities two inequalities I look at maximum S X, W X and V okay if W is not V there exists Y in V such that Y is not in W so I want to show check this step all that I want to say is if W is not equal to V then I have the following look at okay if W is not equal to V then maximum of S X, W X and V can this be 0 can see this is the degree of a polynomial see this S X, W is the unique monic generator of S T X, W can this be 0 if the maximum is 0 can you see that W has to be the whole of V so this cannot be 0 for one thing it is strictly positive and for the other it cannot exceed the dimension of V no it can be equal to V the dimension can be equal to V the degree can be equal to the dimension of V that is possible because this maximum could happen could happen for the characteristic polynomial this maximum could happen for the characteristic polynomial so in which case it could be equal to dimension of V but it is strictly greater than 0 it is strictly greater than 0 otherwise this W will be the whole of V I will take a particular vector Y which attains this maximum let Y be a vector in V for which this maximum is attained in principle this Y can be found out there is a Y there is a Y that attains this maximum all that I will do is consider a new subspace W plus Z Y of T by the way this Y cannot be in W I have not mentioned that this Y cannot be in W note if Y is in W then that degree is 0 if Y is in W that degree is 0 so I am looking at maximum of all those S Y W so Y cannot be in W the degree will otherwise be 0 but it is strictly positive so consider this subspace now since Y does not belong to W remember that we could write down a cyclic basis for this subspace Z Y T we could write down a cyclic basis for this subspace so okay now that cyclic if Y belongs to W then this subspace will be contained in W but Y is not in W so the dimension of this subspace the dimension of this subspace will be strictly greater than the dimension of W 1 dimension of this subspace W that we started with there is at least this is at least one dimensional and that the vector in any basis the vector in that in particular the cyclic basis is independent with I am sorry not W 1 just W the vector in Z Y T in that cyclic basis will be independent with W because it does not belong to W so this dimension is strictly greater than dimension of the subspace W that we started with so what I do now is this is true for any invariant subspace W in particular W 0 I am given an invariant subspace so I will remove the statement we are proving applying W 0 to W what we have is that there exists a vector instead of Y I call it Y 0 there exists Y 0 which does not belong to W 0 such that dimension of W 1 is strictly greater than dimension of W 0 where for me W 1 will be the subspace W 0 plus Z Y 0, T I will call it Y 1 so that I am consistent with my notation if there are K subspaces here that will be W K there is only one subspace here okay what is W 1 is given here what I do now is look at W 1 W 1 for one thing W 0 is invariant under T this is invariant under T cyclic subspace this is invariant under T so the sum will also be invariant under T the W 1 is invariant under T if W 1 is the whole of the space we are done otherwise I can apply this step to W 1 if W 1 is not equal to V then we construct Y 2 such that that is we apply the previous that little result to W 1 Y 2 such that W 2 equals W 0 plus Z Y 1 T plus Z Y 2 T where the dimension of W 2 is strictly greater than the dimension of W 1 this strictly greater than dimension of W 0 every step the dimension increases by at least one V is finite dimensional so this procedure has to terminate okay this procedure terminates at some point because V is finite dimensional and every time we are increasing the dimension by at least one this procedure has to terminate and so I will simply say since this process must terminate we have at after at most dimension V steps we have V equals W 0 plus there is no direct sum just the sum W 0 plus to begin with okay in step 1 W 0 plus Z Y 1 T Z Y 2 T etc Z Y R T I must show that these polynomials satisfy those conditions okay that is easy but this is the first part where we have used W K to denote for any K 1 less than or equal to K less than or equal to R W K is the subspace W 0 Z Y 1 T etc Z Y K T so we apply this we apply the procedure that we started with to this subspace W K to get this formula V is just the sum of these subspaces is it now clear that this these P K's P K's have been chosen like this is it clear that P K must divide okay that comes later we will do that later so is it clear that is it clear that what is the condition that that we have imposed on Y 1 for instance okay you go back go back to this step we have started with the invariance subspace W what is the condition that we have imposed on Y Y is that vector for which this maximum is obtained Y is that vector in V for which this maximum is attained so if you go to first step if you go to the first step Y 1 is the vector for which that maximum is attained okay so if you look at if you look at S I will write that here if you look at little S Y 1 W K minus 1 that is this time W 0 Y 1 W 0 I am calling this P 1 right. So by definition this is a maximum degree among all T hanay letters into W 0 is that not how I see I am applying this for W 0 I am applying this for W 0 among all those among all those among all those X so among all those X and V I look at the subspace W 0 I look at the polynomial that generates that S T and take the maximum I do that for Y 1 I get P 1 P 2 similarly so this is really a consequence of how we have chosen Y 1 Y 2 etc okay so I will just write here that choice of Y K's ensure that P K satisfies the maximum property so as I told you this is an easy consequence of the construction of the vectors I just illustrated for the first vector that this P K satisfies the property that it has maximum degree among all T hanay letters into W K minus 1 comes from the construction of the vectors Y 1 etc Y K okay that is step 1 real is that fine let us move to step 2 I will proceed from step 1 let Y 1 Y 2 etc Y K be non-zero vectors the fact that these are non-zero I have not mentioned but these cannot be 0 otherwise the dimension cannot increase so I will skip that none of these vectors can be 0 because if one of them remember that the Z 0, T we know it is just single term 0 okay so dimension cannot increase if this is the crucial step right if Y is 0 the dimension cannot increase so in none of these vectors can be 0 so I have not mentioned but that is easy to see that Y etc Y 1 etc Y K be the non-zero vectors coming from step 2 non-zero vectors from step 1 satisfying just emphasizing the conditions 1 and 2 satisfying the conditions 1 and 2 for a fixed K let me set F as I fixed K I fixed a K and then I am looking at I am looking at that sub that sub ring that ideal S T Y K comma W K minus 1 my little S is the unique monic generator of that ideal for this step I am calling that polynomial as F for simplicity instead of writing this whole thing I am denoting it by F okay then what do I know about this F this F has a property that this F has a property that if you look at F T Y K thus must belong to W K minus 1 see I have not yet written down what is it that we are going to prove in step 2 okay I have not yet written down what we are proving in step 2 I am just fixing a notation F is this polynomial then by definition this is the polynomial coming from that S T so that is F T Y K must belong to W K minus 1 now it is in W K minus 1 and from the previous step I know what W K is so I know what W K minus 1 is so I can write this F T Y K in terms of these subspaces if okay so I have a representation if F T Y K can be written as so first one is W naught I will call it Y naught it is in W dot I am calling that Y naught plus F T Y K belongs to W K minus 1 W K minus 1 has this plus K minus 1 terms here K minus 1 subspaces so I will use this notation I equals 1 to K minus 1 now I do not know what these I do not know what these vectors are but for one thing I know that these are cyclic subspaces so there is one possibility of what is the basis for this for instance we know that it is Y 1 T Y 1 T square Y 1 etc it is a polynomial in Y 1 so I will write each term as a polynomial in Y 1 I will call that G I I will call it G I T Y I this is the most general expression for any vector in Z Y K, T and remember that each of these cyclic subspaces is invariant under T so is it okay I have I have written I have given a representation for F T Y K I know that it belongs to W K n minus 1 I look at the formula for W K minus 1 the first term is in W naught the rest of the terms are in those K minus 1 subspaces this is the this is the most general formula that one can write down for those terms then what happens what is it that I want to stay mention in step 2 if this happens then F divides each G I okay that is a remarkable property F divides each G I and there exists Z naught in W there exists Z naught and W naught such that there exists Z naught and W naught such that F T Y naught equals F T Z naught this should remind you of the T admissibility property so this is a immediate consequence of T admissibility of W naught the rest we have to show that is quite non-trivial step 2 is probably the most non-trivial part of this proof and even in step 2 the second part is easy consequence of T admissibility of W it is this part that F divides G I that is the most non-trivial let me see so I want to prove step 2 proof of step 2 say I have the polynomials F and G I by Euclidean algorithm there exists polynomials H I such that H I, R I such that I can write the polynomial G I as F I into H I plus R I by Euclidean algorithm where either R I is 0 or degree of R I cannot exceed degree of F here I varies from 1 etc K minus 1 K minus 1 okay I want to show that R I is 0 I want to show that R I is 0 degree of I am sorry it is not F I just F this is F into H I F is the polynomial that I started with G I's are the polynomials that come from the general representation of F T Y K I want to show that each R I is 0 okay we show that each R I equal to 0 if you show that each R I is 0 then it means that F divides G I for all I okay and second one as I mentioned is an easy consequence of T admissibility of W not we need to show that each R I is 0 the proof is by contradiction suppose R I is not 0 we will get a contradiction the proof is by induction on K for proving by induction I need a basis step basis step is K equals 1 basis step is K equals 1 for K equals 1 what do I have what is given what do I need to prove for K equals 1 what I have is that F T Y 1 belongs to W not the question is does F divide G 1 I am sorry just G 0 no for K equal to 1 this is vacuous for K equal to 1 I have just this F T Y K is Y not for K equal to 1 it must be in W K minus 1 that is W not right for K equal to 1 this is W not F T Y 1 is just Y not this simply does not figure F T Y 1 is equal to Y not so the only thing I need to demonstrate is whether this condition is satisfied is verify is this condition is satisfied this is satisfied because W not is T admissible okay this condition is satisfied because W not is T admissible so K equal to 1 is really T admissibility of W not I think I have to stop here and continue tomorrow assume that it is true for K greater than 1 and prove it for prove it for K plus 1 okay and stop here step 2.


If you have a route in your Flask application that processes the image and you want to display the resulting image, you need to pass the processed image's path back to your template when you render it. Here's an example of how you might modify your Flask route to include the processed underscore image variable. Make sure that the actual logic to determine the path of the processed image is implemented in your Flask application, and replace the placeholder, path underscore to underscore process underscore image.jpg, with the correct path based on your application's logic. Let's just continue from what we left off. Hopefully it all makes sense together later. Let me just post on LinkedIn as well, just in case someone wants to join in and ask relevant questions. Ideally, so checking out the website and keep providing any feedback. What's the video called? Okay, let's jump back straight into it. So currently, current application is giving an error. Why am I hearing myself delayed? Because that's the wrong earpiece. I need the real-time one. There's like a six, seven seconds delay from when I speak to the live stream. Okay, so in Python code, let's check this few things. Up your existing code, depth index, existing logic. Now, need the processed image. And this is just a placeholder because we don't have the image yet. And just like the image is also provided in case no image files are found. We already have that. Processed image can go there. It's not currently being used. Return rendered template. Update that. The HTML file. Division class row. Let's minimize this. Division class row column image. This line will be the same. Processed image. I'm not sure why it gave me this line because it's exactly the same as it used to be. Right, make sure. Now we obviously need the image itself. Well, we obviously need the actual logic for processing the image. Now we have it twice. We can get rid of that, can we? Yeah, because that's not needed. Let's see what it says quickly. To implement the logic for determining a path to a processed image in a Flask application, you'll typically have some processing function that takes an original image, applies some kind of feature extraction or other processing, and then saves or identifies the processed images path. Right, so what do you know about a feature extraction from images? Below is an illustrative example of how this could be done within your Flask app. This example assumes you have a processing function that saves the processed image in the same directory as the uploaded image with a modified file name. Okay, first of all, we're using that folder. So we'd like it to be in a separate one. Image folder, a processed image. Wait, yeah, this image folder. Okay, let's add a processed images. A copy path change to separate folders. Okay, we have this in a Python image. I need an absolute folder. Currently we have 40 lines, we have 49. We have processed image in HTML class row. This would be the same. Processed image is not available in JavaScript. It's actually cold. Oops. How does it get? It's not cold. The GGS is called main. JS by mistake, shut down the application. And it's not in the JS folder. Okay, now I'm getting 304, which is much better. I'll deal with logo and other things later. Basic stuff. Change to a separate folder. That's fine. Date when input is changed with that quickly. Agents calls. This is not JavaScript. Is this the whole JavaScript? No, date detected type. Let's read this quickly. This typically involves making a request to a server with a new detector type as a parameter, processing the image server side, and then sending back the new processed image path for display. Okay, so currently I don't have it at all, so it might as well. 40 lines should be fine. It's returning F4 of 4. Let me re-generate some code, not HTML, and the JavaScript. Let's assume that you place an influence template and then get to the Python code in sec. Okay, let's read that and re-generate the whole thing. I've created variables to store the DOM elements for the original and processed images, which eliminates the need to query the DOM every time an image needs to be updated. I've updated the event listener for the image selection dropdown to use the event. Tug it, value which will give us the currently selected value of the dropdown. The update image display function has been defined to update the SRC attributes for both the original and processed image DOM elements. Keep ignoring me. Okay, it feels like I need to start fresh. I've mixed up somewhere, especially the file names. Just check that there's no... Okay, let's start with the info file first. Okay, let's go. Let's just bombard GPT-4. Default version, start with... This one has the confirming... Okay, okay, okay. I've read through your HTML code and noted the structure you're implementing for the feature extraction page. Based on your requirements, here are the necessary updates and comments to be applied to the HTML file for your Flask application. I don't think you know what you're talking about yet because you don't have all the information. Okay, let's do JS first. I don't understand why it's generating stuff and I'm asking not to generate anything at all. Before you proceed with further code generation, make sure to adjust the get underscore processed underscore image underscore path function to match your specific use case because it currently assumes a fixed naming convention for processed images. If your application uses a different naming convention or processing logic, you need to modify this function accordingly. If you confirm that this structure suits your application's requirements and if you need to generate more code for additional roots or logic, like processing images upon changing the detector type, just let me know and I can help you with that. Okay, let's make a process some image to click in with. Let's take code to any processing this stage. Right, OpenCV sounds good. For the application to process images, you typically include a function that uses OpenCV or another library to detect features in the images according to the selected detector type. Here is a simplified example of what such a function might look like using OpenCV for feature detection. The process underscore image underscore with underscore fast function takes an image path for Zimbut, uses the fast algorithm to find key points and then draws those key points on the image. Finally, it saves the processed image to a file and returns the path to the saved image. Okay, let's do the other functions as well and then we will try to integrate it all. Absolutely, you can create functions similar to the one for fast detection for Harris and Sheet and Marzi feature detectors using OpenCV. Here are examples of how you might implement these detectors. Integrate all into the current app.py. To integrate the processing functions into your app.py, you'll want to add routes that handle the processing requests based on the detector type selected by the user. You'll also need to ensure that OpenCV is imported, import CV2, and the NumPy is available, import NumPy as NB since the processing functions depend on these libraries. Write the rest of the file, remain unchanged, process stage folder. How many lines of code? Only 50 lines can integrate the whole thing. It's necessary all the necessary code for app to run with no errors. Certainly. To create a complete app.py with integrated image processing features using OpenCV for feature detection algorithms like Fast, Harris, and Sheet and Marzi, follow these steps. Define routes for rendering a home page and for processing images. Downloading files from the server. Now is the full example code with the necessary imports, routes, utility functions, and placeholder functions for image processing. The secure underscore file name function is a utility provided by WebZug, which is a comprehensive WSGI web application library that Flask is built upon. It's used to sanitize the file name provided by the user, ensuring it is safe to use within the file system. This function escapes special characters and removes any characters that might have significance to the file system, such as slashes or dots, which could potentially be used in a malicious manner to access or manipulate files outside of the intended directories. When dealing with file uploads or any other form of input that specifies a file name, you should always sanitize the input before using it to access or store files on the server. This is to prevent a wide variety of attacks, including directory traversal attacks. Yeah, I think it's missing some of the context that I'm taking the files from an online folder. Can I save this? Make sure to implement the actual processing logic inside process underscore Harris, process underscore she underscore tamazi, and process underscore fast functions according to the feature extraction algorithms you want to apply. You need to write code that reads the image from disk using openCV, processes it using the relevant detector, and then saves the processed image back to the static, processed underscore images directory. I think those errors are okay. I wasn't able to get the first image the first time around. Some folder issues to HTML quickly. See if it's generating the whole code. HTML, about 105, the main index, more, but that code should remain exactly the same. I don't know why I'm changing it. Write this bit here. Main.js has been called okay. If I'm under the label, it's not populated as to JS with HTML. Do I need placeholders? Remember, the fetch images and fetch detector types functions are placeholders. You should replace them with the actual logic to fetch image file names and detector types for your server. The way you populate the drop-downs will depend on how your flash back-end serves this data. If it's provided within the page render context, you might not need fetching logic and instead use the server-ended values. The update image display function is updated to change the SRC attribute for both the original and processed image displays when the user selects a different image. The update detector type function is intended to handle the logic when the detector type is changed, which might include making an Ajax call to the server to process the image with the new detector type and then update the display accordingly. Okay, I'm giving up. Why is it called scrape.js? It should be called... Oh, come on. This is not the folder structure that I asked for. Wrong. We have static main.js style. Yeah, that makes sense. Let's find the folders I need you to regenerate the files. Just generate all calls for me. This is wrong. Okay, it's really out of whack. HGPD new chat default starts from index. Yeah, this way we'll have some description of the application not ready yet. Right, now it's actually behaving. Yeah, let's start the application again. Let's just fix it. It was working just a second ago. No, that's okay. Your application is trying to render a 404 HTML template when a page is not found but it can't find the 404 HTML file in your templates directory. Ensure that you have created a 404 HTML file and test it in the correct templates folder within your application structure. How about we remove that whole thing? Let's remove the script.js. It's not right because it's not called script.js. Just rename it. You win. Yeah, those are different script.js files. One is in static folder. No, it's actually getting it. It's okay. Now, Python is not plotting the entries. Labels like name, ID, image select, search for death in JavaScript, select image and check the drop-downs are not too late. Why isn't it hypothetical? You're following aspects of your code to troubleshoot. HTML template. Ensure that the index HTML template is correctly set up to trade over image underscore files and detector underscore types to populate the options. Data passing in root confirm that the correct context is being passed to render underscore template in the index root and that the image underscore files and detector underscore types variables contain the correct data before being passed to template populated by the flask. That's why I gave it a flask. Based on the snippet you provided, it looks like the template is prepared to have its select options populated by the server, but you have not included any ginger to template logic to actually populate these options. You need to loop over the options provided to the template from flask and render them accordingly. Here is how you can modify your drop-down menus to be populated with the images and detector types provided by your flask context. Now, when flask renders the template, it will replace the percent for image and image underscore files percent and percent for detector and detector underscore types percent blocks with option elements corresponding to each item in the image underscore files and detector underscore types context variables. This is already happening, is it? On page load as the image is selected by default To ensure the first image is selected and displayed by default when the page loads, you can modify your flask view to pass the first image in the list of the template and then adjust the HTML template to mark it as selected in the drop-down. You also need to ensure that the image is displayed on the page, and by clicking an IMG tag, the reference is the selected image. Here is how you can modify the flask view in the HTML template. You can make sure the selected underscore image is set to the first image file in the list of available. It seems you are already doing this based on the previous code you showed. Sorry for that. Can I go for a bit longer? I guess we are already doing that now in the HTML. You can adjust the select element for images to set the selected attribute on the option that matches selected underscore image. Additionally, you need to display the image. Big, which really used to be a 50% I can swear it was a too big plus responsive image. This is not. Control the display size with CSS to make sure the images fit within the user's viewport without causing layout issues. Serves scaled-down versions of the images of the original size are largely large for web display, which can save bandwidth and improve load times. In your HTML template, you can add a class to your IMG tag and then define the size in CSS to ensure that images are never displayed too large, regardless of their actual size. You could also use inline styles, but using a CSS class is generally a cleaner and more maintainable approach. This CSS ensures that the image is responsive and its size is controlled. The max width, 100% rule means the image will scale down on smaller screens of your size. If you want to serve smaller versions of the original images, you would need to create these scaled-down versions when the images are uploaded or processed. This can be done using an image processing library such as Pillow, Pillfork, in Python. Remember that you should call this resize function either when the image is uploaded or before you send it for processing, depending on when you need the image to be resized. The resized images should be saved to a directory that your Flask app serves, such as the static images or static processed underscore images directories. This is not the standard error because there's no when it starts. Now this shouldn't be or selected image. This is wrong. And if processed which is not does not exist don't. In the Flask template to check if processed underscore image underscore path is available before displaying the processed image. Here's an example of how you can do it. Be an easy fix for this. That's more like it. Okay, why is it giving all that stuff? Start it again. Just script 3 or 4. Yes, we actually want a code for actually processing the image. No, this should be in there. A Python script we're going to hit the limit of prompts, what is it, 53 hours or something. To make your code functional for the process underscore harris, process underscore she underscore to marzi and process underscore fast functions, you need to implement the respective algorithms using open CV functions and then save the processed images to the static processed underscore images directory. Below are the example implementations for each of these functions. We're unlikely to work still generating a copy relative. Remember to change the extensions in a replace method if you plan on using different image formats or the original images have varying extensions. Additionally, the image path needs to be returned in a web friendly format relative to the static folder. The above code snippets include steps to convert the saved image path to a relative path usable by the Flask application. Lastly, these snippets assume the original images are JPEGs, so adjust the extensions if using different formats. Also, ensure that the static images and static processed underscore images directories are correctly set up as per the comments at the beginning of your Python file. Check that the application has permission to write files to the static processed underscore images directory. If you're running in a unix-like system, permissions can be set with the chmod command. Check that the application has permission to write files to the static processed underscore images directory. If you're running in a unix-like system, permissions can be set with the chmod command.