Artifact af380e88dcaf5ddb323da0cb6a641785ea9cb5ec39a38ea9f7a09a60293ece0a:
- Executable file
r38/packages/trigsimp/trigsimp.rlg
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 36401) [annotate] [blame] [check-ins using] [more...]
Tue Feb 10 12:29:44 2004 run on Linux % Test file for TrigSimp package %-------------------------TrigSimp-------------------------- trigsimp(tan(x+y), keepalltrig); - (tan(x) + tan(y)) ---------------------- tan(x)*tan(y) - 1 trigsimp(ws, keepalltrig, combine); tan(x + y) trigsimp(sin(5x-9y)); 4 9 4 7 - 4096*cos(x)*sin(x) *sin(y) + 9216*cos(x)*sin(x) *sin(y) 4 5 4 3 - 6912*cos(x)*sin(x) *sin(y) + 1920*cos(x)*sin(x) *sin(y) 4 2 9 - 144*cos(x)*sin(x) *sin(y) + 3072*cos(x)*sin(x) *sin(y) 2 7 2 5 - 6912*cos(x)*sin(x) *sin(y) + 5184*cos(x)*sin(x) *sin(y) 2 3 2 9 - 1440*cos(x)*sin(x) *sin(y) + 108*cos(x)*sin(x) *sin(y) - 256*cos(x)*sin(y) 7 5 3 + 576*cos(x)*sin(y) - 432*cos(x)*sin(y) + 120*cos(x)*sin(y) 5 8 5 6 - 9*cos(x)*sin(y) + 4096*cos(y)*sin(x) *sin(y) - 7168*cos(y)*sin(x) *sin(y) 5 4 5 2 5 + 3840*cos(y)*sin(x) *sin(y) - 640*cos(y)*sin(x) *sin(y) + 16*cos(y)*sin(x) 3 8 3 6 - 5120*cos(y)*sin(x) *sin(y) + 8960*cos(y)*sin(x) *sin(y) 3 4 3 2 3 - 4800*cos(y)*sin(x) *sin(y) + 800*cos(y)*sin(x) *sin(y) - 20*cos(y)*sin(x) 8 6 + 1280*cos(y)*sin(x)*sin(y) - 2240*cos(y)*sin(x)*sin(y) 4 2 + 1200*cos(y)*sin(x)*sin(y) - 200*cos(y)*sin(x)*sin(y) + 5*cos(y)*sin(x) trigsimp(ws, combine); sin(5*x - 9*y) trigsimp(cos(10x), cos); 10 8 6 4 2 512*cos(x) - 1280*cos(x) + 1120*cos(x) - 400*cos(x) + 50*cos(x) - 1 trigsimp(cos(10x), sin); 10 8 6 4 2 - 512*sin(x) + 1280*sin(x) - 1120*sin(x) + 400*sin(x) - 50*sin(x) + 1 trigsimp((sin(x-a)+sin(x+a))/(cos(x-a)+cos(x+a))); sin(x) -------- cos(x) trigsimp(cos(6x+4y), sin); 5 3 5 256*cos(x)*cos(y)*sin(x) *sin(y) - 128*cos(x)*cos(y)*sin(x) *sin(y) 3 3 3 - 256*cos(x)*cos(y)*sin(x) *sin(y) + 128*cos(x)*cos(y)*sin(x) *sin(y) 3 + 48*cos(x)*cos(y)*sin(x)*sin(y) - 24*cos(x)*cos(y)*sin(x)*sin(y) 6 4 6 2 6 4 4 - 256*sin(x) *sin(y) + 256*sin(x) *sin(y) - 32*sin(x) + 384*sin(x) *sin(y) 4 2 4 2 4 2 2 - 384*sin(x) *sin(y) + 48*sin(x) - 144*sin(x) *sin(y) + 144*sin(x) *sin(y) 2 4 2 - 18*sin(x) + 8*sin(y) - 8*sin(y) + 1 trigsimp(ws, expon); 12*i*x + 8*i*y e + 1 --------------------- 6*i*x + 4*i*y 2*e trigsimp(ws, hyp); 5 3 256*cosh(i*x)*cosh(i*y)*sinh(i*x) *sinh(i*y) 5 + 128*cosh(i*x)*cosh(i*y)*sinh(i*x) *sinh(i*y) 3 3 + 256*cosh(i*x)*cosh(i*y)*sinh(i*x) *sinh(i*y) 3 + 128*cosh(i*x)*cosh(i*y)*sinh(i*x) *sinh(i*y) 3 + 48*cosh(i*x)*cosh(i*y)*sinh(i*x)*sinh(i*y) 6 4 + 24*cosh(i*x)*cosh(i*y)*sinh(i*x)*sinh(i*y) + 256*sinh(i*x) *sinh(i*y) 6 2 6 4 4 + 256*sinh(i*x) *sinh(i*y) + 32*sinh(i*x) + 384*sinh(i*x) *sinh(i*y) 4 2 4 2 4 + 384*sinh(i*x) *sinh(i*y) + 48*sinh(i*x) + 144*sinh(i*x) *sinh(i*y) 2 2 2 4 2 + 144*sinh(i*x) *sinh(i*y) + 18*sinh(i*x) + 8*sinh(i*y) + 8*sinh(i*y) + 1 trigsimp(ws, combine); cosh(6*i*x + 4*i*y) trigsimp(ws, trig, combine); cos(6*x + 4*y) trigsimp(sqrt(1-cos(2x))); sqrt(2)*abs(sin(x)) trigsimp(sin(x)^20*cos(x)^20, sin); 20 20 18 16 14 12 sin(x) *(sin(x) - 10*sin(x) + 45*sin(x) - 120*sin(x) + 210*sin(x) 10 8 6 4 2 - 252*sin(x) + 210*sin(x) - 120*sin(x) + 45*sin(x) - 10*sin(x) + 1) trigsimp(sin(x)^20*cos(x)^20, cos); 20 20 18 16 14 12 cos(x) *(cos(x) - 10*cos(x) + 45*cos(x) - 120*cos(x) + 210*cos(x) 10 8 6 4 2 - 252*cos(x) + 210*cos(x) - 120*cos(x) + 45*cos(x) - 10*cos(x) + 1) trigsimp(sin(x)^20*cos(x)^20, compact); 20 20 cos(x) *sin(x) trigsimp(sin(x)^10, combine); - cos(10*x) + 10*cos(8*x) - 45*cos(6*x) + 120*cos(4*x) - 210*cos(2*x) + 126 ------------------------------------------------------------------------------ 512 trigsimp(ws, hyp); 10 - sinh(i*x) trigsimp(ws, expon); 20*i*x 18*i*x 16*i*x 14*i*x 12*i*x 10*i*x ( - e + 10*e - 45*e + 120*e - 210*e + 252*e 8*i*x 6*i*x 4*i*x 2*i*x 10*i*x - 210*e + 120*e - 45*e + 10*e - 1)/(1024*e ) trigsimp(ws, trig); 10 sin(x) int(sin(x+y)*cos(x-y)*tan(x), x); int(cos(x - y)*sin(x + y)*tan(x),x) int(trigsimp(sin(x+y)*cos(x-y)*tan(x)), x); 2 2 cos(x) *x - cos(x)*sin(x) - 2*cos(y)*log(cos(x))*sin(y) + sin(x) *x --------------------------------------------------------------------- 2 % int(sin(x+y)*cos(x-y)/tan(x), x) hangs int(trigsimp(sin(x+y)*cos(x-y)/tan(x)), x); x 2 (cos(x)*sin(x) - 2*cos(y)*log(tan(---) + 1)*sin(y) 2 x + 2*cos(y)*log(tan(---))*sin(y) + x)/2 2 trigsimp(2tan(x)*(sec(x)^2 - tan(x)^2 - 1)); 0 on rationalize; df(sqrt(1+cos(x)), x, 4); 4 2 2 2 (sqrt(cos(x) + 1)*( - 4*cos(x) - 20*cos(x) *sin(x) + 12*cos(x) 2 4 2 - 4*cos(x)*sin(x) + 8*cos(x) - 15*sin(x) + 16*sin(x) ))/(16 4 3 2 *(cos(x) + 4*cos(x) + 6*cos(x) + 4*cos(x) + 1)) off rationalize; trigsimp(ws); sqrt(cos(x) + 1) ------------------ 16 df(2cos((x+y)/2)*cos((x-y)/2), x); x - y x + y x + y x - y - (cos(-------)*sin(-------) + cos(-------)*sin(-------)) 2 2 2 2 trigsimp(ws, combine); - sin(x) df(int(1/cos(x), x), x); x 2 - (tan(---) + 1) 2 -------------------- x 2 tan(---) - 1 2 trigsimp(ws, combine); 1 -------- cos(x) trigsimp(cos(100x)); 100 633825300114114700748351602688*sin(x) 98 - 15845632502852867518708790067200*sin(x) 96 + 192128294097091018664344079564800*sin(x) 94 - 1505335087771022414277335056384000*sin(x) 92 + 8567473526884295537508113973248000*sin(x) 90 - 37750993877408064336851542202122240*sin(x) 88 + 134036108580690866727917044786790400*sin(x) 86 - 394078512785625681900511864396185600*sin(x) 84 + 978503372439851812055958467641344000*sin(x) 82 - 2082455895192505138478065456775168000*sin(x) 80 + 3842131126630171980492030767750184960*sin(x) 78 - 6200783636440931286187342812099379200*sin(x) 76 + 8816739233064449172547628060953804800*sin(x) 74 - 11108623702136905456127648087408640000*sin(x) 72 + 12460295938318846194767764735918080000*sin(x) 70 - 12489614281703125832873100652943769600*sin(x) 68 + 11221137831217652115471926367879168000*sin(x) 66 - 9058026923994972189597820080095232000*sin(x) 64 + 6581798018959761296303294062264320000*sin(x) 62 - 4310885252184171141438414824407040000*sin(x) 60 + 2547463753712583633893763260298035200*sin(x) 58 - 1358954443662228159129584379363328000*sin(x) 56 + 654531379770880870350000868032512000*sin(x) 54 - 284578860769948204500000377405440000*sin(x) 52 + 111631674825053695350740279623680000*sin(x) 50 - 39472960218138986676021762874933248*sin(x) 48 + 12566106098549963273941439584665600*sin(x) 46 - 3595780740528756614156758967910400*sin(x) 44 + 923024074019658505866132324352000*sin(x) 42 - 212040013118649088525828358144000*sin(x) 40 + 43468202689323063147794813419520*sin(x) 38 - 7925478751208973645460484915200*sin(x) 36 + 1280241627320751027747867852800*sin(x) 34 - 182395347175955031090266112000*sin(x) 32 + 22799418396994378886283264000*sin(x) 30 28 - 2485387148331694929142087680*sin(x) + 234623135747458180159897600*sin(x) 26 24 - 19023497493037149742694400*sin(x) + 1312104559685287280640000*sin(x) 22 20 - 76111992112891822080000*sin(x) + 3662889620432918937600*sin(x) 18 16 - 143850563845029888000*sin(x) + 4517474603507712000*sin(x) 14 12 - 110586893598720000*sin(x) + 2042087523840000*sin(x) 10 8 6 - 27227833651200*sin(x) + 246628928000*sin(x) - 1386112000*sin(x) 4 2 + 4165000*sin(x) - 5000*sin(x) + 1 trigsimp(ws, combine); cos(100*x) trigsimp(sinh(3a+4b-5c)*cosh(3a-5b-6c)); 5 10 16384*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 5 8 + 36864*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 5 6 + 28672*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 5 4 + 8960*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 5 2 + 960*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 5 + 16*cosh(a)*cosh(b)*cosh(c)*sinh(a) 3 10 + 16384*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 3 8 + 36864*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 3 6 + 28672*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 3 4 + 8960*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 3 2 + 960*cosh(a)*cosh(b)*cosh(c)*sinh(a) *sinh(c) 3 + 16*cosh(a)*cosh(b)*cosh(c)*sinh(a) 10 + 3072*cosh(a)*cosh(b)*cosh(c)*sinh(a)*sinh(c) 8 + 6912*cosh(a)*cosh(b)*cosh(c)*sinh(a)*sinh(c) 6 + 5376*cosh(a)*cosh(b)*cosh(c)*sinh(a)*sinh(c) 4 + 1680*cosh(a)*cosh(b)*cosh(c)*sinh(a)*sinh(c) 2 + 180*cosh(a)*cosh(b)*cosh(c)*sinh(a)*sinh(c) 5 11 + 3*cosh(a)*cosh(b)*cosh(c)*sinh(a) + 16384*cosh(a)*sinh(a) *sinh(b)*sinh(c) 5 9 + 45056*cosh(a)*sinh(a) *sinh(b)*sinh(c) 5 7 + 45056*cosh(a)*sinh(a) *sinh(b)*sinh(c) 5 5 + 19712*cosh(a)*sinh(a) *sinh(b)*sinh(c) 5 3 5 + 3520*cosh(a)*sinh(a) *sinh(b)*sinh(c) + 176*cosh(a)*sinh(a) *sinh(b)*sinh(c) 3 11 + 16384*cosh(a)*sinh(a) *sinh(b)*sinh(c) 3 9 + 45056*cosh(a)*sinh(a) *sinh(b)*sinh(c) 3 7 + 45056*cosh(a)*sinh(a) *sinh(b)*sinh(c) 3 5 + 19712*cosh(a)*sinh(a) *sinh(b)*sinh(c) 3 3 3 + 3520*cosh(a)*sinh(a) *sinh(b)*sinh(c) + 176*cosh(a)*sinh(a) *sinh(b)*sinh(c) 11 + 3072*cosh(a)*sinh(a)*sinh(b)*sinh(c) 9 7 + 8448*cosh(a)*sinh(a)*sinh(b)*sinh(c) + 8448*cosh(a)*sinh(a)*sinh(b)*sinh(c) 5 3 + 3696*cosh(a)*sinh(a)*sinh(b)*sinh(c) + 660*cosh(a)*sinh(a)*sinh(b)*sinh(c) 6 11 + 33*cosh(a)*sinh(a)*sinh(b)*sinh(c) - 16384*cosh(b)*sinh(a) *sinh(c) 6 9 6 7 - 45056*cosh(b)*sinh(a) *sinh(c) - 45056*cosh(b)*sinh(a) *sinh(c) 6 5 6 3 - 19712*cosh(b)*sinh(a) *sinh(c) - 3520*cosh(b)*sinh(a) *sinh(c) 6 4 11 - 176*cosh(b)*sinh(a) *sinh(c) - 24576*cosh(b)*sinh(a) *sinh(c) 4 9 4 7 - 67584*cosh(b)*sinh(a) *sinh(c) - 67584*cosh(b)*sinh(a) *sinh(c) 4 5 4 3 - 29568*cosh(b)*sinh(a) *sinh(c) - 5280*cosh(b)*sinh(a) *sinh(c) 4 2 11 - 264*cosh(b)*sinh(a) *sinh(c) - 9216*cosh(b)*sinh(a) *sinh(c) 2 9 2 7 - 25344*cosh(b)*sinh(a) *sinh(c) - 25344*cosh(b)*sinh(a) *sinh(c) 2 5 2 3 - 11088*cosh(b)*sinh(a) *sinh(c) - 1980*cosh(b)*sinh(a) *sinh(c) 2 8 - 99*cosh(b)*sinh(a) *sinh(c) + 128*cosh(b)*sinh(b) *sinh(c) 6 4 + 224*cosh(b)*sinh(b) *sinh(c) + 120*cosh(b)*sinh(b) *sinh(c) 2 11 9 + 20*cosh(b)*sinh(b) *sinh(c) - 512*cosh(b)*sinh(c) - 1408*cosh(b)*sinh(c) 7 5 3 - 1408*cosh(b)*sinh(c) - 616*cosh(b)*sinh(c) - 110*cosh(b)*sinh(c) 6 10 - 5*cosh(b)*sinh(c) - 16384*cosh(c)*sinh(a) *sinh(b)*sinh(c) 6 8 - 36864*cosh(c)*sinh(a) *sinh(b)*sinh(c) 6 6 - 28672*cosh(c)*sinh(a) *sinh(b)*sinh(c) 6 4 - 8960*cosh(c)*sinh(a) *sinh(b)*sinh(c) 6 2 6 - 960*cosh(c)*sinh(a) *sinh(b)*sinh(c) - 16*cosh(c)*sinh(a) *sinh(b) 4 10 - 24576*cosh(c)*sinh(a) *sinh(b)*sinh(c) 4 8 - 55296*cosh(c)*sinh(a) *sinh(b)*sinh(c) 4 6 - 43008*cosh(c)*sinh(a) *sinh(b)*sinh(c) 4 4 - 13440*cosh(c)*sinh(a) *sinh(b)*sinh(c) 4 2 4 - 1440*cosh(c)*sinh(a) *sinh(b)*sinh(c) - 24*cosh(c)*sinh(a) *sinh(b) 2 10 - 9216*cosh(c)*sinh(a) *sinh(b)*sinh(c) 2 8 - 20736*cosh(c)*sinh(a) *sinh(b)*sinh(c) 2 6 - 16128*cosh(c)*sinh(a) *sinh(b)*sinh(c) 2 4 - 5040*cosh(c)*sinh(a) *sinh(b)*sinh(c) 2 2 2 - 540*cosh(c)*sinh(a) *sinh(b)*sinh(c) - 9*cosh(c)*sinh(a) *sinh(b) 9 7 5 + 128*cosh(c)*sinh(b) + 288*cosh(c)*sinh(b) + 216*cosh(c)*sinh(b) 3 10 + 60*cosh(c)*sinh(b) - 512*cosh(c)*sinh(b)*sinh(c) 8 6 - 1152*cosh(c)*sinh(b)*sinh(c) - 896*cosh(c)*sinh(b)*sinh(c) 4 2 - 280*cosh(c)*sinh(b)*sinh(c) - 30*cosh(c)*sinh(b)*sinh(c) + 4*cosh(c)*sinh(b) trigsimp(ws, combine); sinh(9*b + c) + sinh(6*a - b - 11*c) -------------------------------------- 2 trigsimp(sec(20x-y), keepalltrig); 20 20 20 19 (csc(x) *csc(y)*sec(x) *sec(y))/(csc(x) *csc(y) + 20*csc(x) *sec(x)*sec(y) 18 2 17 3 - 190*csc(x) *csc(y)*sec(x) - 1140*csc(x) *sec(x) *sec(y) 16 4 15 5 + 4845*csc(x) *csc(y)*sec(x) + 15504*csc(x) *sec(x) *sec(y) 14 6 13 7 - 38760*csc(x) *csc(y)*sec(x) - 77520*csc(x) *sec(x) *sec(y) 12 8 11 9 + 125970*csc(x) *csc(y)*sec(x) + 167960*csc(x) *sec(x) *sec(y) 10 10 9 11 - 184756*csc(x) *csc(y)*sec(x) - 167960*csc(x) *sec(x) *sec(y) 8 12 7 13 + 125970*csc(x) *csc(y)*sec(x) + 77520*csc(x) *sec(x) *sec(y) 6 14 5 15 - 38760*csc(x) *csc(y)*sec(x) - 15504*csc(x) *sec(x) *sec(y) 4 16 3 17 + 4845*csc(x) *csc(y)*sec(x) + 1140*csc(x) *sec(x) *sec(y) 2 18 19 20 - 190*csc(x) *csc(y)*sec(x) - 20*csc(x)*sec(x) *sec(y) + csc(y)*sec(x) ) trigsimp(csc(10a-9b), keepalltrig); 10 9 10 9 10 8 ( - csc(a) *csc(b) *sec(a) *sec(b) )/(9*csc(a) *csc(b) *sec(b) 10 6 3 10 4 5 - 84*csc(a) *csc(b) *sec(b) + 126*csc(a) *csc(b) *sec(b) 10 2 7 10 9 9 9 - 36*csc(a) *csc(b) *sec(b) + csc(a) *sec(b) - 10*csc(a) *csc(b) *sec(a) 9 7 2 9 5 4 + 360*csc(a) *csc(b) *sec(a)*sec(b) - 1260*csc(a) *csc(b) *sec(a)*sec(b) 9 3 6 9 8 + 840*csc(a) *csc(b) *sec(a)*sec(b) - 90*csc(a) *csc(b)*sec(a)*sec(b) 8 8 2 8 6 2 3 - 405*csc(a) *csc(b) *sec(a) *sec(b) + 3780*csc(a) *csc(b) *sec(a) *sec(b) 8 4 2 5 - 5670*csc(a) *csc(b) *sec(a) *sec(b) 8 2 2 7 8 2 9 + 1620*csc(a) *csc(b) *sec(a) *sec(b) - 45*csc(a) *sec(a) *sec(b) 7 9 3 7 7 3 2 + 120*csc(a) *csc(b) *sec(a) - 4320*csc(a) *csc(b) *sec(a) *sec(b) 7 5 3 4 + 15120*csc(a) *csc(b) *sec(a) *sec(b) 7 3 3 6 - 10080*csc(a) *csc(b) *sec(a) *sec(b) 7 3 8 6 8 4 + 1080*csc(a) *csc(b)*sec(a) *sec(b) + 1890*csc(a) *csc(b) *sec(a) *sec(b) 6 6 4 3 - 17640*csc(a) *csc(b) *sec(a) *sec(b) 6 4 4 5 + 26460*csc(a) *csc(b) *sec(a) *sec(b) 6 2 4 7 6 4 9 - 7560*csc(a) *csc(b) *sec(a) *sec(b) + 210*csc(a) *sec(a) *sec(b) 5 9 5 5 7 5 2 - 252*csc(a) *csc(b) *sec(a) + 9072*csc(a) *csc(b) *sec(a) *sec(b) 5 5 5 4 - 31752*csc(a) *csc(b) *sec(a) *sec(b) 5 3 5 6 + 21168*csc(a) *csc(b) *sec(a) *sec(b) 5 5 8 4 8 6 - 2268*csc(a) *csc(b)*sec(a) *sec(b) - 1890*csc(a) *csc(b) *sec(a) *sec(b) 4 6 6 3 + 17640*csc(a) *csc(b) *sec(a) *sec(b) 4 4 6 5 - 26460*csc(a) *csc(b) *sec(a) *sec(b) 4 2 6 7 4 6 9 + 7560*csc(a) *csc(b) *sec(a) *sec(b) - 210*csc(a) *sec(a) *sec(b) 3 9 7 3 7 7 2 + 120*csc(a) *csc(b) *sec(a) - 4320*csc(a) *csc(b) *sec(a) *sec(b) 3 5 7 4 + 15120*csc(a) *csc(b) *sec(a) *sec(b) 3 3 7 6 - 10080*csc(a) *csc(b) *sec(a) *sec(b) 3 7 8 2 8 8 + 1080*csc(a) *csc(b)*sec(a) *sec(b) + 405*csc(a) *csc(b) *sec(a) *sec(b) 2 6 8 3 - 3780*csc(a) *csc(b) *sec(a) *sec(b) 2 4 8 5 + 5670*csc(a) *csc(b) *sec(a) *sec(b) 2 2 8 7 2 8 9 - 1620*csc(a) *csc(b) *sec(a) *sec(b) + 45*csc(a) *sec(a) *sec(b) 9 9 7 9 2 - 10*csc(a)*csc(b) *sec(a) + 360*csc(a)*csc(b) *sec(a) *sec(b) 5 9 4 3 9 6 - 1260*csc(a)*csc(b) *sec(a) *sec(b) + 840*csc(a)*csc(b) *sec(a) *sec(b) 9 8 8 10 - 90*csc(a)*csc(b)*sec(a) *sec(b) - 9*csc(b) *sec(a) *sec(b) 6 10 3 4 10 5 + 84*csc(b) *sec(a) *sec(b) - 126*csc(b) *sec(a) *sec(b) 2 10 7 10 9 + 36*csc(b) *sec(a) *sec(b) - sec(a) *sec(b) ) trigsimp(ws, combine); 1 ----------------- sin(10*a - 9*b) trigsimp(cosh(50*acosh(x))-cos(50*acos(x))); 0 trigsimp(cos(n*acos(x))-cosh(n*acosh(x)), trig); 0 trigsimp((2tan(log(x))*(sec(log(x))^2 - tan(log(x))^2 - 1))/x); 0 trigsimp(sech(10x), keepalltrig); 10 10 10 8 2 6 4 (csch(x) *sech(x) )/(csch(x) + 45*csch(x) *sech(x) + 210*csch(x) *sech(x) 4 6 2 8 10 + 210*csch(x) *sech(x) + 45*csch(x) *sech(x) + sech(x) ) trigsimp(ws, combine); 1 ------------ cosh(10*x) trigsimp(csch(3x-5y), keepalltrig); 3 5 3 5 3 4 ( - csch(x) *csch(y) *sech(x) *sech(y) )/(5*csch(x) *csch(y) *sech(y) 3 2 3 3 5 + 10*csch(x) *csch(y) *sech(y) + csch(x) *sech(y) 2 5 2 3 2 - 3*csch(x) *csch(y) *sech(x) - 30*csch(x) *csch(y) *sech(x)*sech(y) 2 4 - 15*csch(x) *csch(y)*sech(x)*sech(y) 4 2 + 15*csch(x)*csch(y) *sech(x) *sech(y) 2 2 3 2 5 + 30*csch(x)*csch(y) *sech(x) *sech(y) + 3*csch(x)*sech(x) *sech(y) 5 3 3 3 2 - csch(y) *sech(x) - 10*csch(y) *sech(x) *sech(y) 3 4 - 5*csch(y)*sech(x) *sech(y) ) trigsimp(ws, combine); 1 ----------------- sinh(3*x - 5*y) off precise; trigsimp((sinh(x)+cosh(x))^n+(cosh(x)-sinh(x))^n, expon); 2*n*x e + 1 ------------ n*x e on precise; trigsimp(ws, hyp); 2*cosh(n*x) load_package taylor; taylor(sin(x+a)*cos(x+b), x, 0, 4); cos(b)*sin(a) + (cos(a)*cos(b) - sin(a)*sin(b))*x 2 - (cos(a)*sin(b) + cos(b)*sin(a))*x 2*( - cos(a)*cos(b) + sin(a)*sin(b)) 3 + --------------------------------------*x 3 cos(a)*sin(b) + cos(b)*sin(a) 4 5 + -------------------------------*x + O(x ) 3 trigsimp(ws, combine); sin(a - b) + sin(a + b) 2 2*cos(a + b) 3 ------------------------- + cos(a + b)*x - sin(a + b)*x - --------------*x 2 3 sin(a + b) 4 5 + ------------*x + O(x ) 3 %-----------------------TrigFactorize----------------------- on nopowers; % for comparison with version 2.0 trigfactorize(sin(x)**2, x); {sin(x),sin(x)} trigfactorize(1+cos(x), x); {cos(x) + 1} trigfactorize(1+cos(x), x/2); x x {2,cos(---),cos(---)} 2 2 trigfactorize(1+cos(x), x/6); {2, x 2 - 4*sin(---) + 1, 6 x 2 - 4*sin(---) + 1, 6 x cos(---), 6 x cos(---)} 6 trigfactorize(sin(x)*(1-cos(x)), x); {sin(x)*( - cos(x) + 1)} trigfactorize(sin(x)*(1-cos(x)), x/2); {4, x cos(---), 2 x sin(---), 2 x sin(---), 2 x sin(---)} 2 trigfactorize(tan(x), x); {tan(x)} trigfactorize(sin(x*3), x); 2 { - 4*sin(x) + 3,sin(x)} trigfactorize(sin(4x)-1, x); {-1, 2 2*cos(x)*sin(x) + 2*sin(x) - 1, 2 2*cos(x)*sin(x) + 2*sin(x) - 1} trigfactorize(sin(x)**4-1, x); 2 {-1,sin(x) + 1,cos(x),cos(x)} trigfactorize(cos(x)**4-1, x); 2 {sin(x) - 2,sin(x),sin(x)} trigfactorize(sin(x)**10-cos(x)**6, x); {-1, 2 5 cos(x)*sin(x) - cos(x) - sin(x) , 2 5 cos(x)*sin(x) - cos(x) + sin(x) } trigfactorize(sin(x)*cos(y), x); {cos(y),sin(x)} trigfactorize(sin(2x)*cos(y)**2, y/2); {2*cos(x)*sin(x), y y cos(---) + sin(---), 2 2 y y cos(---) + sin(---), 2 2 y y cos(---) - sin(---), 2 2 y y cos(---) - sin(---)} 2 2 trigfactorize(sin(y)**4-x**2, y); 2 2 {sin(y) - x,sin(y) + x} trigfactorize(sin(x), x+1); ***** TrigGCD/Factorize error: last arg must be [number*]variable. trigfactorize(sin(x), 2x); ***** TrigGCD/Factorize error: basis not possible. trigfactorize(sin(x)*cosh(x), x/2); {2, x cos(---), 2 x sin(---), 2 x x cosh(---) - i*sinh(---), 2 2 x x cosh(---) + i*sinh(---)} 2 2 trigfactorize(1+cos(2x)+2cos(x)*cosh(x), x/2); {4, x x x x cos(---)*cosh(---) + i*sin(---)*sinh(---), 2 2 2 2 x x x x cos(---)*cosh(---) - i*sin(---)*sinh(---), 2 2 2 2 x x cos(---) + sin(---), 2 2 x x cos(---) - sin(---)} 2 2 %-------------------------TrigGCD--------------------------- triggcd(sin(x), cos(x), x); 1 triggcd(1-cos(x)^2, sin(x)^2, x); 2 - sin(x) triggcd(sin(x)^4-1, cos(x)^2, x); 2 - sin(x) + 1 triggcd(sin(5x+1), cos(x), x); 1 triggcd(1-cos(2x), sin(2x), x); sin(x) triggcd(-5+cos(2x)-6sin(x), -7+cos(2x)-8sin(x), x/2); x x 2*cos(---)*sin(---) + 1 2 2 triggcd(1-2cosh(x)+cosh(2x), 1+2cosh(x)+cosh(2x), x/2); x 2 2*sinh(---) + 1 2 triggcd(1+cos(2x)+2cos(x)*cosh(x), 1+2cos(x)*cosh(x)+cosh(2x), x/2); x 2 x 2 - sin(---) + sinh(---) + 1 2 2 triggcd(-1+2a*b+cos(2x)-2a*sin(x)+2b*sin(x), -1-2a*b+cos(2x)-2a*sin(x)-2b*sin(x), x/2); x x 2*cos(---)*sin(---) + a 2 2 triggcd(sin(x)^10-1, cos(x), x); cos(x) triggcd(sin(5x)+sin(3x), cos(x), x); cos(x) triggcd(sin(3x)+sin(5x), sin(5x)+sin(7x), x); 2 sin(x)*(sin(x) - 1) %----------------------------------------------------------- % New facilities in version 2 %----------------------------------------------------------- % TrigSimp applied to non-scalars data structures: trigsimp( sin(2x) = cos(2x) ); 2 2*cos(x)*sin(x)= - 2*sin(x) + 1 trigsimp( { sin(2x), cos(2x) } ); 2 {2*cos(x)*sin(x), - 2*sin(x) + 1} trigsimp( { sin(2x) = cos(2x) } ); 2 {2*cos(x)*sin(x)= - 2*sin(x) + 1} trigsimp( mat((sin(2x),cos(2x)), (csc(2x),sec(2x))) ); [ 2 ] [ 2*cos(x)*sin(x) - 2*sin(x) + 1] [ ] [ 1 - 1 ] [----------------- --------------- ] [ 2*cos(x)*sin(x) 2 ] [ 2*sin(x) - 1 ] % An amusing identify: trigsimp(csc x - cot x - tan(x/2)); 0 % which could be DERIVED like this: trigsimp(csc x - cot x, x/2, tan); x tan(---) 2 % A silly illustration of multiple additional trig arguments: trigsimp(csc x - cot x, x/2, x/3); x 5 x 3 x 16*sin(---) - 24*sin(---) + 9*sin(---) 6 6 6 ------------------------------------------------------------ x x 4 x x 2 x 16*cos(---)*sin(---) - 16*cos(---)*sin(---) + 3*cos(---) 6 6 6 6 6 % A more useful illustration of multiple additional trig arguments: trigsimp(csc x - cot x + csc y - cot y, x/2, y/2, tan); x y tan(---) + tan(---) 2 2 %----------------------------------------------------------- % New TrigFactorize facility: off nopowers; % REDUCE 3.7 default, gives more compact output ... trigfactorize(sin(x)^2, x); {{sin(x),2}} trigfactorize(1+cos(x), x); {{cos(x) + 1,1}} trigfactorize(1+cos(x), x/2); x {{2,1},{cos(---),2}} 2 trigfactorize(1+cos(x), x/6); x x 2 {{2,1},{cos(---),2},{ - 4*sin(---) + 1,2}} 6 6 trigfactorize(sin(x)*(1-cos(x)), x); {{sin(x)*( - cos(x) + 1),1}} trigfactorize(sin(x)*(1-cos(x)), x/2); x x {{4,1},{sin(---),3},{cos(---),1}} 2 2 trigfactorize(tan(x), x); {{tan(x),1}} trigfactorize(sin(3x), x); 2 {{sin(x),1},{ - 4*sin(x) + 3,1}} trigfactorize(sin(4x) - 1, x); 2 {{-1,1},{2*cos(x)*sin(x) + 2*sin(x) - 1,2}} trigfactorize(sin(x)^4 - 1, x); 2 {{-1,1},{cos(x),2},{sin(x) + 1,1}} trigfactorize(cos(x)^4 - 1, x); 2 {{sin(x),2},{sin(x) - 2,1}} trigfactorize(sin(x)^10 - cos(x)^6, x); {{-1,1}, 2 5 {cos(x)*sin(x) - cos(x) + sin(x) ,1}, 2 5 {cos(x)*sin(x) - cos(x) - sin(x) ,1}} trigfactorize(sin(x)*cos(y), x); {{cos(y),1},{sin(x),1}} trigfactorize(sin(2x)*cos(y)^2, y/2); {{2*cos(x)*sin(x),1}, y y {cos(---) - sin(---),2}, 2 2 y y {cos(---) + sin(---),2}} 2 2 trigfactorize(sin(y)^4 - x^2, y); 2 2 {{sin(y) + x,1},{sin(y) - x,1}} trigfactorize(sin(x), x+1); ***** TrigGCD/Factorize error: last arg must be [number*]variable. trigfactorize(sin(x), 2x); ***** TrigGCD/Factorize error: basis not possible. trigfactorize(sin(x)*cosh(x), x/2); {{2,1}, x x {cosh(---) + i*sinh(---),1}, 2 2 x x {cosh(---) - i*sinh(---),1}, 2 2 x {sin(---),1}, 2 x {cos(---),1}} 2 trigfactorize(1 + cos(2x) + 2cos(x)*cosh(x), x/2); {{4,1}, x x {cos(---) - sin(---),1}, 2 2 x x {cos(---) + sin(---),1}, 2 2 x x x x {cos(---)*cosh(---) - i*sin(---)*sinh(---), 2 2 2 2 1}, x x x x {cos(---)*cosh(---) + i*sin(---)*sinh(---), 2 2 2 2 1}} end; Time for test: 2890 ms, plus GC time: 70 ms