## How to get the solution with higher order polynomi...

Hi all guys! I am doing the error analysis but now I meet one question: how to get the explict solution of eq11? If it is complex, I just wanna the real part. Welcome all guys discussion!

## 2nd Order Gaussian Curve Smoothing...

Please write the code for 2nd Order Gausian Smoothing of the curve with the following data:

X := Vector[row](781, [0, 0.000115771, 0.000231541, 0.000347312, 0.000463082, 0.000578853, 0.000694623, 0.000810394, 0.000926164, 0.001041935, 0.001157705, 0.001273476, 0.001389246, 0.001505017, 0.001620787, 0.001736558, 0.001852328, 0.001968099, 0.002083869, 0.00219964, 0.00231541, 0.002431181, 0.002546952, 0.002662722, 0.002778493, 0.002894263, 0.003010034, 0.003125804, 0.003241575, 0.003357345, 0.003473116, 0.003588886, 0.003704657, 0.003820427, 0.003936198, 0.004051968, 0.004167739, 0.004283509, 0.00439928, 0.00451505, 0.004630821, 0.004746591, 0.004862362, 0.004978132, 0.005093903, 0.005209674, 0.005325444, 0.005441215, 0.005556985, 0.005672756, 0.005788526, 0.005904297, 0.006020067, 0.006135838, 0.006251608, 0.006367379, 0.006483149, 0.013008131, 0.013123901, 0.013239672, 0.013355442, 0.013471213, 0.013586983, 0.013702754, 0.013818524, 0.013934295, 0.014050065, 0.014165836, 0.014281606, 0.014397377, 0.014513148, 0.014628918, 0.014744689, 0.014860459, 0.01497623, 0.015092, 0.015207771, 0.015323541, 0.015439312, 0.015555082, 0.015670853, 0.015786623, 0.015902394, 0.016018164, 0.016133935, 0.016249705, 0.016365476, 0.016481246, 0.016597017, 0.016712787, 0.016828558, 0.023353539, 0.02346931, 0.02358508, 0.023700851, 0.023816621, 0.023932392, 0.024048163, 0.024163933, 0.024279704, 0.024395474, 0.024511245, 0.024627015, 0.024742786, 0.024858556, 0.024974327, 0.025090097, 0.031615079, 0.031730849, 0.03184662, 0.03196239, 0.032078161, 0.032193931, 0.032309702, 0.032425472, 0.032541243, 0.032657013, 0.032772784, 0.032888554, 0.033004325, 0.033120095, 0.039645077, 0.039760847, 0.039876618, 0.039992388, 0.040108159, 0.040223929, 0.0403397, 0.040455471, 0.040571241, 0.047096222, 0.047211993, 0.047327764, 0.047443534, 0.047559305, 0.047675075, 0.047790846, 0.047906616, 0.054431598, 0.054547368, 0.054663139, 0.054778909, 0.05489468, 0.05501045, 0.055126221, 0.055241991, 0.055357762, 0.061882743, 0.061998514, 0.062114284, 0.062230055, 0.062345825, 0.062461596, 0.062577366, 0.062693137, 0.069218118, 0.069333889, 0.069449659, 0.06956543, 0.0696812, 0.069796971, 0.076321952, 0.076437723, 0.076553493, 0.076669264, 0.076785034, 0.076900805, 0.077016575, 0.077132346, 0.077248116, 0.083773098, 0.083888868, 0.084004639, 0.084120409, 0.08423618, 0.08435195, 0.090876932, 0.090992702, 0.091108473, 0.091224243, 0.091340014, 0.097864995, 0.097980766, 0.098096536, 0.098212307, 0.098328077, 0.098443848, 0.098559619, 0.1050846, 0.10520037, 0.105316141, 0.105431912, 0.105547682, 0.105663453, 0.105779223, 0.112304205, 0.112419975, 0.112535746, 0.112651516, 0.112767287, 0.112883057, 0.119408039, 0.119523809, 0.11963958, 0.11975535, 0.119871121, 0.119986891, 0.120102662, 0.126627643, 0.126743414, 0.126859184, 0.126974955, 0.127090725, 0.127206496, 0.133731477, 0.133847248, 0.133963018, 0.134078789, 0.134194559, 0.13431033, 0.1344261, 0.140951082, 0.141066852, 0.141182623, 0.141298393, 0.141414164, 0.141529934, 0.148054916, 0.148170686, 0.148286457, 0.148402227, 0.148517998, 0.148633768, 0.148749539, 0.15527452, 0.155390291, 0.155506061, 0.155621832, 0.155737602, 0.155853373, 0.162378354, 0.162494125, 0.162609895, 0.162725666, 0.162841436, 0.162957207, 0.163072977, 0.169597959, 0.169713729, 0.1698295, 0.16994527, 0.170061041, 0.170176811, 0.176701793, 0.176817563, 0.176933334, 0.177049104, 0.177164875, 0.177280646, 0.183805627, 0.183921397, 0.184037168, 0.184152938, 0.184268709, 0.18438448, 0.18450025, 0.191025231, 0.191141002, 0.191256773, 0.191372543, 0.191488314, 0.191604084, 0.198129066, 0.198244836, 0.198360607, 0.198476377, 0.198592148, 0.198707918, 0.2052329, 0.20534867, 0.205464441, 0.205580211, 0.205695982, 0.205811752, 0.212336734, 0.212452504, 0.212568275, 0.212684045, 0.212799816, 0.212915586, 0.219440568, 0.219556338, 0.219672109, 0.219787879, 0.21990365, 0.22001942, 0.220135191, 0.226660172, 0.226775943, 0.226891713, 0.227007484, 0.227123254, 0.227239025, 0.233764006, 0.233879777, 0.233995547, 0.234111318, 0.234227088, 0.234342859, 0.24086784, 0.240983611, 0.241099381, 0.241215152, 0.241330922, 0.247855904, 0.247971674, 0.248087445, 0.248203215, 0.248318986, 0.248434756, 0.254959738, 0.255075508, 0.255191279, 0.255307049, 0.25542282, 0.25553859, 0.262063572, 0.262179342, 0.262295113, 0.262410883, 0.262526654, 0.269051635, 0.269167406, 0.269283176, 0.269398947, 0.269514717, 0.276039699, 0.276155469, 0.27627124, 0.27638701, 0.276502781, 0.283027762, 0.283143533, 0.283259303, 0.283375074, 0.283490844, 0.290015826, 0.290131596, 0.290247367, 0.290363137, 0.290478908, 0.290594678, 0.29711966, 0.29723543, 0.297351201, 0.297466971, 0.297582742, 0.304107723, 0.304223494, 0.304339264, 0.304455035, 0.304570805, 0.304686576, 0.311211557, 0.311327328, 0.311443098, 0.311558869, 0.31167464, 0.31179041, 0.318315391, 0.318431162, 0.318546933, 0.318662703, 0.318778474, 0.318894244, 0.325419225, 0.325534996, 0.325650767, 0.325766537, 0.325882308, 0.325998078, 0.33252306, 0.33263883, 0.332754601, 0.332870371, 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0.594364816, 0.594480587, 0.594596357, 0.601121339, 0.601237109, 0.60135288, 0.607877861, 0.607993632, 0.608109402, 0.614634384, 0.614750154, 0.614865925, 0.621390906, 0.621506677, 0.628031658, 0.628147428, 0.628263199, 0.63478818, 0.634903951, 0.635019721, 0.641544703, 0.641660473, 0.648185455, 0.648301225, 0.648416996, 0.654941977, 0.655057748, 0.655173518, 0.6616985, 0.66181427, 0.668339252, 0.668455022, 0.668570793, 0.675095774, 0.675211545, 0.681736526, 0.681852297, 0.681968067, 0.688493049, 0.688608819, 0.695133801, 0.695249571, 0.695365342, 0.701890323, 0.702006094, 0.708531075, 0.708646845, 0.715171827, 0.715287597, 0.715403368, 0.721928349, 0.72204412, 0.728569101, 0.728684872, 0.735209853, 0.735325624, 0.741966376, 0.748607128, 0.75524788, 0.761888631, 0.768529383, 0.775170135, 0.781695117, 0.788335869, 0.794976621, 0.801501602, 0.808142354, 0.814783106, 0.821423858, 0.827948839, 0.834589591, 0.841230343, 0.847871095, 0.854511847, 0.861152599, 0.867793351, 0.874318332, 0.880959084, 0.887599836, 0.894240588, 0.90076557, 0.907406322, 0.913931303, 0.920572055, 0.927097036, 0.933622018, 0.94026277, 0.946787751, 0.953312733, 0.959953484, 0.966478466, 0.973119218, 0.97975997, 0.986284951, 0.992925703, 0.999450685, 1.006091437, 1.012732188, 1.019488711, 1.026129463, 1.032885985, 1.039526737, 1.046051719, 1.0525767, 1.059101682, 1.065626663, 1.072151644, 1.078676626, 1.091610818, 1.085201607, 1.0981358, 1.111069992, 1.104660781, 1.117594973, 1.124119955, 1.137054147, 1.130644936, 1.143579128, 1.15010411, 1.163038302, 1.156629091, 1.169563284, 1.176088265, 1.182613246, 1.195547439, 1.189138228, 1.20207242, 1.208597402, 1.221531594, 1.215122383, 1.228056575, 1.240990768, 1.234581557, 1.25392496, 1.247515749, 1.266859152, 1.260449941, 1.279793345, 1.273384134, 1.292727537, 1.286318326, 1.31207094, 1.305661729, 1.299252518, 1.331414343, 1.325005132, 1.318595921, 1.350757746, 1.344348536, 1.337939325, 1.37010115, 1.363691939, 1.357282728, 1.389444553, 1.383035342, 1.376626131, 1.415197167, 1.408787956, 1.402378745, 1.395969534, 1.43454057, 1.428131359, 1.421722148, 1.453883973, 1.447474762, 1.441065552, 1.466818166, 1.460408955, 1.486161569, 1.479752358, 1.473343147, 1.499095761, 1.49268655, 1.518439164, 1.512029954, 1.505620743, 1.537782568, 1.531373357, 1.524964146, 1.563535182, 1.557125971, 1.55071676, 1.544307549, 1.595697007, 1.948319377, 1.589287796, 1.941910166, 1.582878585, 1.935500955, 1.576469374, 1.929091744, 1.570060163, 1.922682533, 1.916273322, 1.909864111, 1.9034549, 1.897045689, 1.890636478, 1.884227268, 1.659904886, 1.653495675, 1.647086464, 1.640677254, 1.634268043, 1.627858832, 1.621449621, 1.61504041, 1.608631199, 1.602221988, 1.877933827, 1.871524616, 1.865115405, 1.858706194, 1.852296984, 1.845887773, 1.839478562, 1.833069351, 1.82666014, 1.820250929, 1.813841718, 1.807432507, 1.801023296, 1.794614086, 1.788204875, 1.781795664, 1.775386453, 1.768977242, 1.762568031, 1.75615882, 1.749749609, 1.743340398, 1.736931187, 1.730521977, 1.724112766, 1.717703555, 1.711294344, 1.704885133, 1.698475922, 1.692066711, 1.6856575, 1.679248289, 1.672839079, 1.666429868])

Y := Vector[row](782, [0, 0.006409211, 0.012818422, 0.019227633, 0.025636844, 0.032046054, 0.038455265, 0.044864476, 0.051273687, 0.057682898, 0.064092109, 0.07050132, 0.076910531, 0.083319742, 0.089728953, 0.096138163, 0.102547374, 0.108956585, 0.115365796, 0.121775007, 0.128184218, 0.134593429, 0.14100264, 0.147411851, 0.153821061, 0.160230272, 0.166639483, 0.173048694, 0.179457905, 0.185867116, 0.192276327, 0.198685538, 0.205094749, 0.21150396, 0.21791317, 0.224322381, 0.230731592, 0.237140803, 0.243550014, 0.249959225, 0.256368436, 0.262777647, 0.269186858, 0.275596068, 0.282005279, 0.28841449, 0.294823701, 0.301232912, 0.307642123, 0.314051334, 0.320460545, 0.326869756, 0.333278967, 0.339688177, 0.346097388, 0.352506599, 0.35891581, 0.365209251, 0.371618461, 0.378027672, 0.384436883, 0.390846094, 0.397255305, 0.403664516, 0.410073727, 0.416482938, 0.422892149, 0.429301359, 0.43571057, 0.442119781, 0.448528992, 0.454938203, 0.461347414, 0.467756625, 0.474165836, 0.480575047, 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1.471918866, 1.478328077, 1.484737288, 1.491146499, 1.497439939, 1.50384915, 1.510258361, 1.516667572, 1.523076783, 1.529485994, 1.535779434, 1.542188645, 1.548597856, 1.555007067, 1.561416277, 1.567825488, 1.574234699, 1.58052814, 1.586937351, 1.593346561, 1.599755772, 1.606164983, 1.612574194, 1.618867634, 1.625276845, 1.631686056, 1.638095267, 1.644504478, 1.650913689, 1.657207129, 1.66361634, 1.670025551, 1.676434762, 1.682843973, 1.689253184, 1.695662395, 1.701955835, 1.708365046, 1.714774257, 1.721183468, 1.727592679, 1.73400189, 1.74029533, 1.746704541, 1.753113752, 1.759522963, 1.765932173, 1.772341384, 1.778634825, 1.785044036, 1.791453247, 1.797862457, 1.804271668, 1.810680879, 1.81697432, 1.823383531, 1.829792741, 1.836201952, 1.842611163, 1.849020374, 1.855313814, 1.861723025, 1.868132236, 1.874541447, 1.880950658, 1.887359869, 1.89376908, 1.90006252, 1.906471731, 1.912880942, 1.919290153, 1.925699364, 1.932108575, 1.938402015, 1.944811226, 1.951220437, 1.957629648, 1.964038859, 1.97044807, 1.97674151, 1.983150721, 1.989559932, 1.995969143, 2.002378353, 2.008671794, 2.015081005, 2.021490216, 2.027899427, 2.034308637, 2.040717848, 2.047011289, 2.0534205, 2.05982971, 2.066238921, 2.072648132, 2.079057343, 2.085350784, 2.091759994, 2.098169205, 2.104578416, 2.110987627, 2.117281068, 2.123690278, 2.130099489, 2.1365087, 2.142917911, 2.149211351, 2.155620562, 2.162029773, 2.168438984, 2.174848195, 2.181141635, 2.187550846, 2.193960057, 2.200369268, 2.206778479, 2.213071919, 2.21948113, 2.225890341, 2.232299552, 2.238708763, 2.245117974, 2.251411414, 2.257820625, 2.264229836, 2.270639047, 2.277048258, 2.283341698, 2.289750909, 2.29616012, 2.302569331, 2.308978542, 2.315387753, 2.321681193, 2.328090404, 2.334499615, 2.340908826, 2.347318037, 2.353727247, 2.360020688, 2.366429899, 2.37283911, 2.379248321, 2.385657531, 2.392066742, 2.398360183, 2.404769394, 2.411178604, 2.417587815, 2.423997026, 2.430406237, 2.436699678, 2.443108888, 2.449518099, 2.45592731, 2.462336521, 2.468629962, 2.475039172, 2.481448383, 2.487857594, 2.494266805, 2.500676016, 2.506969456, 2.513378667, 2.519787878, 2.526197089, 2.5326063, 2.539015511, 2.545308951, 2.551718162, 2.558127373, 2.564536584, 2.570945795, 2.577355006, 2.583648446, 2.590057657, 2.596466868, 2.602876079, 2.60928529, 2.61557873, 2.621987941, 2.628397152, 2.634806363, 2.641215574, 2.647624784, 2.653918225, 2.660327436, 2.666736647, 2.673145858, 2.679555068, 2.685848509, 2.69225772, 2.698666931, 2.705076141, 2.711485352, 2.717778793, 2.724188004, 2.730597215, 2.737006425, 2.743415636, 2.749824847, 2.756118288, 2.762527499, 2.768936709, 2.77534592, 2.781639361, 2.788048572, 2.794457782, 2.800866993, 2.807276204, 2.813569645, 2.819978856, 2.826388066, 2.832797277, 2.839206488, 2.845499929, 2.851909139, 2.85831835, 2.864727561, 2.871021002, 2.877430213, 2.883839423, 2.890248634, 2.896542075, 2.902951286, 2.909360496, 2.915769707, 2.922178918, 2.928472359, 2.93488157, 2.94129078, 2.947699991, 2.953993432, 2.960402643, 2.966811853, 2.973221064, 2.979514505, 2.985923716, 2.992332927, 2.998742137, 3.005035578, 3.011444789, 3.017854, 3.024263211, 3.030556651, 3.036965862, 3.043375073, 3.049784284, 3.056077724, 3.062486935, 3.068896146, 3.075305357, 3.081598797, 3.088008008, 3.094417219, 3.10082643, 3.10711987, 3.113529081, 3.119938292, 3.126347503, 3.132640943, 3.139050154, 3.145459365, 3.151868576, 3.158162016, 3.164571227, 3.170980438, 3.177273878, 3.183683089, 3.1900923, 3.196501511, 3.202794951, 3.209204162, 3.215613373, 3.222022584, 3.228316024, 3.234725235, 3.241134446, 3.247427887, 3.253837098, 3.260246308, 3.266539749, 3.27294896, 3.279358171, 3.285767381, 3.292060822, 3.298470033, 3.304879244, 3.311172684, 3.317581895, 3.323991106, 3.330284546, 3.336693757, 3.343102968, 3.349396408, 3.355805619, 3.36221483, 3.36850827, 3.374917481, 3.381326692, 3.387620133, 3.394029344, 3.400438554, 3.406731995, 3.413141206, 3.419550417, 3.425843857, 3.432253068, 3.438662279, 3.444955719, 3.45136493, 3.457774141, 3.464067581, 3.470476792, 3.476886003, 3.483179443, 3.489588654, 3.495997865, 3.502291306, 3.508700517, 3.515109727, 3.521403168, 3.527812379, 3.534105819, 3.54051503, 3.546924241, 3.553217681, 3.559626892, 3.566036103, 3.572329543, 3.578738754, 3.585032195, 3.591441406, 3.597850616, 3.604144057, 3.610553268, 3.616962479, 3.623255919, 3.62966513, 3.63595857, 3.642367781, 3.648776992, 3.655070432, 3.661479643, 3.667773084, 3.674182295, 3.680591505, 3.686884946, 3.693294157, 3.699587597, 3.705996808, 3.712406019, 3.718699459, 3.72510867, 3.731402111, 3.737811321, 3.744104762, 3.750513973, 3.756923184, 3.763216624, 3.769625835, 3.775919275, 3.782328486, 3.788621926, 3.795031137, 3.807733789, 3.82043644, 3.833139091, 3.845841742, 3.858544394, 3.871247045, 3.877540485, 3.890243137, 3.902945788, 3.909239228, 3.92194188, 3.934644531, 3.947347182, 3.953640622, 3.966343274, 3.979045925, 3.991748576, 4.004451228, 4.017153879, 4.02985653, 4.03614997, 4.048852622, 4.061555273, 4.074257924, 4.080551365, 4.093254016, 4.099547456, 4.112250108, 4.118543548, 4.124836988, 4.13753964, 4.14383308, 4.15012652, 4.162829172, 4.169122612, 4.181825263, 4.194527914, 4.200821355, 4.213524006, 4.219817446, 4.232520098, 4.245222749, 4.264334611, 4.277037262, 4.296149125, 4.308851776, 4.315145216, 4.321438657, 4.327732097, 4.334025537, 4.340318978, 4.346612418, 4.352790088, 4.352905858, 4.359083528, 4.365261198, 4.365376969, 4.371554639, 4.377848079, 4.384025749, 4.384141519, 4.390319189, 4.396612629, 4.402790299, 4.40290607, 4.40908374, 4.41537718, 4.42167062, 4.42784829, 4.427964061, 4.434141731, 4.440435171, 4.446612841, 4.446728611, 4.452906281, 4.459083951, 4.459199722, 4.465261621, 4.465377391, 4.471439291, 4.471555061, 4.477616961, 4.477732731, 4.483794631, 4.483910401, 4.48985653, 4.4899723, 4.490088071, 4.495918429, 4.4960342, 4.49614997, 4.501980329, 4.502096099, 4.50221187, 4.508042228, 4.508157998, 4.508273769, 4.514104127, 4.514219898, 4.514335668, 4.520050256, 4.520166026, 4.520281797, 4.520397568, 4.526112155, 4.526227926, 4.526343696, 4.532174055, 4.532289825, 4.532405596, 4.538351724, 4.538467495, 4.544413624, 4.544529394, 4.544645165, 4.550591294, 4.550707064, 4.556653193, 4.556768963, 4.556884734, 4.562715092, 4.562830863, 4.562946633, 4.568661221, 4.568776992, 4.568892762, 4.569008533, 4.574491579, 4.574533412, 4.57460735, 4.574649182, 4.57472312, 4.574764953, 4.574838891, 4.574880723, 4.574954661, 4.574996494, 4.575112264, 4.575228035, 4.575343805, 4.575459576, 4.575575346, 4.575691117, 4.579743085, 4.579858856, 4.579974626, 4.580090397, 4.580206167, 4.580321938, 4.580437708, 4.580553479, 4.580669249, 4.58078502, 4.582216098, 4.582331869, 4.582447639, 4.58256341, 4.58267918, 4.582794951, 4.582910721, 4.583026492, 4.583142262, 4.583258033, 4.583373803, 4.583489574, 4.583605344, 4.583721115, 4.583836885, 4.583952656, 4.584068427, 4.584184197, 4.584299968, 4.584415738, 4.584531509, 4.584647279, 4.58476305, 4.58487882, 4.584994591, 4.585110361, 4.585226132, 4.585341902, 4.585457673, 4.585573443, 4.585689214, 4.585804984, 4.585920755, 4.586036525])

## silently testing for the Maple version...

(Tested on Maple 2021.1 and 2024.0, on Mac)

I want to write a Maple procedure that takes advantages of the latest features but doesn't break on older versions of Maple.

So I can write something like this:

if version() >= VERSION then new_method else old_method end if

This works, but it has the problem that the version( ) command not only returns a version number but also writes three lines to the screen, like this:

``` User Interface: 1794891
Kernel: 1794891
Library: 1794891
```

I don't want those lines to appear every time the procedure is used but I don't know how to make them go away.  Is there a way, or is there a better approach to achieving what I want?

Thanks, Brendan.

## How do I solve a system of differential equations ...

Hello everyone

I need help solving a system of equations as below. I'm looking for a way to do it, but I don't understand the general concept of how such an equation is calculated. So far I've been using a package in LabVIEW that worked similarly to Simulink and that was clear to me, whereas here I'm overwhelmed by the multitude of options and that's why I'm asking for help.

I need to solve these equations analogously to Matlab-Simulink, i.e., a time interval and integration step, and a numerical procedure in symbolic versions.

Help_me.mw

## How to draw a number of circles inscribed in a squ...

I have a square with length of side is \$a\$. How to draw a number of circles inscribed in a square so that the sum of the radii of the circle is greatest? In the below picture is twenty circles inscribed in a square. We can consider number of circles are 5, 6, ... We consider number of the circles is fixed.

How can I tell Maple to do that.

## Maple 2024 crash calling solve. Reproducible each ...

I am getting Maple server crash each time running this solve command.

Could others reproduce it? I am using windows 10. Maple 2024.  Why does it happen?

Will report it to Maplesoft in case it is not known. Worksheet below.

 > restart;

 > interface(version);

 > Physics:-Version();

 > sol:=(3^(1/2)*u(x)-1/3*3^(1/2)+(3*u(x)^2-2*u(x)-1)^(1/2))^(1/3*3^(1/2)) = x^(1/3*3^(1/2))*c__1;

 > eval(sol,u(x) = u);

 > timelimit(30,[solve(%,u)]);

This bug seems to have been introduced in Maple 2023 since it crashes there also.

But not in Maple 2022. No crash there. Same PC.

 > restart;
 > interface(version);

 > Physics:-Version();

 > sol:=(3^(1/2)*u(x)-1/3*3^(1/2)+(3*u(x)^2-2*u(x)-1)^(1/2))^(1/3*3^(1/2)) = x^(1/3*3^(1/2))*c__1;

 > eval(sol,u(x) = u);

 > solve(%,u);

## to simplify or not simplify before calling integra...

Is this a valid behvior by int?

int(A,x,method=_RETURNVERBOSE) hangs.

But  int(simplify(A),x,method=_RETURNVERBOSE) returns in few seconds with "default" result same as int(A,x)

Should this have happen? I try to avoid calling simplify unless neccessary because it can add csgn's and signums and so on to the result.

But the question is: Should one really need to simplify the integrand to get the result in this example? Does this mean one should call simplify on the integrand to avoid the hang that can show up?

This only happens when using method=_RETURNVERBOSE

Just trying to find out if this is normal behavior and can be expected sometimes.

 > interface(version);

 > restart;

 > A:=exp(-1/2*cos(2*x))*exp(-sin(x)^2); int(A,x);

 > int(A,x,method=_RETURNVERBOSE);  #hangs
 > int(simplify(A),x,method=_RETURNVERBOSE)

## solve elliptic PDEs...

As Maple is not equipped to handle numerical solutions of elliptic PDEs, can anyone help top solve PDEs by finite differences or any other numerical solver?

pde.mw

## Where is the code that simplifies this ...

Can't figure out what code makes this simplification.
If this simplification works, it will be a part of a larger simplication procedure ( if it not conflicts hopefully)
vereenvouding_hoe_-vraag_MPF.mw

## PDEtools:-Solve vs. solve. RootOf form difference...

I was trying to find out why my solution was not validating for this ode. It turned out because I was using solve instead of PDEtools:-Solve. It took me sometime to find this.

This made huge difference on odetest to verify the solution.

This is very simple ode. We just need to integrate once. But first we have to solve for y'(x).

And here comes the difference. When I used solve to solve for y'(x), odetest did not verify the solution.

When using PDEtools:-Solve, it did.

The difference is how each returned the solution for y'(x). Both have RootOf but written differently and this made the difference.

1) Why solutions are written differently?

2) Is this to be expected? I have thought Solve uses same engine as solve below the cover.

3) is it possible to make solve give the same form as Solve or change to that form?

I am now changing more of my code to use PDEtools:-Solve because of this.

 > interface(version);

 > Physics:-Version();

Using solve

 > restart;

 > ode:=x-ln(diff(y(x),x))-sin(diff(y(x),x))=0; RHS:=solve(ode,diff(y(x),x));

 > mysol:= y(x) = Int(RHS,x)+c__1;

 > odetest(mysol,ode);

using PDEtools:-Solve (now it verifies) with no extra effort

 > restart;

 > ode:=x-ln(diff(y(x),x))-sin(diff(y(x),x))=0; RHS:=PDEtools:-Solve(ode,diff(y(x),x)): RHS:=rhs(%);

 > mysol:= y(x) = Int(RHS,x)+c__1;

 > odetest(mysol,ode);

Update

Here is a counter example. Where now it is the other way around.

Using solve makes odetest happy, but when using PDEtools:-Solve odetest does not verify the solution.  Same exact ODE.

 > interface(version);

 > Physics:-Version()

Example, using solve works

 > ode:=exp(diff(y(x), x) - y(x)) - diff(y(x), x)^2 + 1 = 0; RHS:=solve(ode,diff(y(x),x)); RHS:=eval(RHS,y(x)=y); mysol:=Intat(eval(1/RHS,y=_a),_a=y(x))=x+c__1; odetest(mysol,ode);

Example, using PDEtools:-Solve fails

 > ode:=exp(diff(y(x), x) - y(x)) - diff(y(x), x)^2 + 1 = 0; RHS:=rhs(PDEtools:-Solve(ode,diff(y(x),x))); RHS:=eval(RHS,y(x)=y); mysol:=Intat(eval(1/RHS,y=_a),_a=y(x))=x+c__1; odetest(mysol,ode);

 >

So now I have no idea which to use. Sometimes solve works and sometimes Solve works. I  guess I have to now solve the ode both ways each time and see which works.

## N-Soft set : Membership function, ...

Dear all

I have a data, how can I study this data using N-soft set : Normalized the data, membership function, analyse the risk, ..... compute the risk, interpret the results

Cancer_patient.xlsx

N_soft_set.mw

## Visualize a surface : saddle surface...

Maybe someone get the code working ?

```with(plots):
with(VectorCalculus):

# Example 1: Vector Field and Visualization
V := [x, y, z]:
print("Vector Field V:", V):
fieldplot3d([V[1], V[2], V[3]], x = -2..2, y = -2..2, z = -2..2, arrows = slim, title = "Vector Field in 3D"):

# Example 2: Tangent Vector to a Curve
curve := [cos(t), sin(t), t]:
print("Curve:", curve):
tangent := diff(curve, t):
print("Tangent Vector:", tangent):
plot3d([cos(t), sin(t), t], t = 0..2*Pi, labels = [x, y, z], title = "Curve in 3D"):

# Example 3: Curvature of a Surface
u := 'u': v := 'v':
surface := [u, v, u^2 - v^2]:
print("Surface:", surface):

# Compute the first fundamental form
ru := [diff(surface[1], u), diff(surface[2], u), diff(surface[3], u)]:
rv := [diff(surface[1], v), diff(surface[2], v), diff(surface[3], v)]:
E := ru[1]^2 + ru[2]^2 + ru[3]^2:
F := ru[1]*rv[1] + ru[2]*rv[2] + ru[3]*rv[3]:
G := rv[1]^2 + rv[2]^2 + rv[3]^2:
firstFundamentalForm := Matrix([[E, F], [F, G]]):
print("First Fundamental Form:", firstFundamentalForm):

# Compute the second fundamental form
ruu := [diff(surface[1], u, u), diff(surface[2], u, u), diff(surface[3], u, u)]:
ruv := [diff(surface[1], u, v), diff(surface[2], u, v), diff(surface[3], u, v)]:
rvv := [diff(surface[1], v, v), diff(surface[2], v, v), diff(surface[3], v, v)]:
normal := CrossProduct(ru, rv):
normal := eval(normal / sqrt(normal[1]^2 + normal[2]^2 + normal[3]^2)):
L := ruu[1]*normal[1] + ruu[2]*normal[2] + ruu[3]*normal[3]:
M := ruv[1]*normal[1] + ruv[2]*normal[2] + ruv[3]*normal[3]:
N := rvv[1]*normal[1] + rvv[2]*normal[2] + rvv[3]*normal[3]:
secondFundamentalForm := Matrix([[L, M], [M, N]]):
print("Second Fundamental Form:", secondFundamentalForm):

# Compute the Christoffel symbols
# Ensure DifferentialGeometry package is loaded
with(DifferentialGeometry):
DGsetup([u, v], N):
Gamma := Christoffel(firstFundamentalForm):
print("Christoffel Symbols:", Gamma):

# Visualize the surface
plot3d([u, v, u^2 - v^2], u = -2..2, v = -2..2, labels = [u, v, z], title = "Saddle Surface in 3D"):```

## should int() result match exactly what is given as...

Simple question. I hope it has simple answer. I have always thought that what int() returns should match exactly what "default" result shows when using int() with the option _RETURNVERBOSE

I mean exact match. But this below shows that int() result underwent some simplification as it is not the same as default.

```restart;

integrand:=sin(x)/(sin(x) + 1);
maple_result_1 :=int(integrand,x);
maple_result_2 := int(integrand,x,'method'=':-_RETURNVERBOSE')[1]

```

Ofcourse maple_result_2 can be made the same as maple_result_1

```simplify(rhs(maple_result_2)) assuming 0<x and x<Pi;
```

But this is beside the point. Why is "default" is not excatly the same as int() result?  It seems that int() does something more after obtaining the :"default" result as shown.

Should default not match exactly result from int() ?

Maple 2024.

## Numeric Formatting Causes Maple to Hang...

I put together the attached worksheet to help me determine the cheapest way to buy "refreshments" for a party by comparing price and volume of different bottle size options.  The spreadsheet works fine as is.  However, when I right click on the output of line (14) and format pct_difference as percent with 2 decimal places and execute the worksheet, Maple hangs on that line and progresses no further.  This doesn't happen in Maple 2018 but the problem does show up in Maple 2024.  Suggestions please?

cost_comparison_-_liquid_(v01MP).mw