Artifact 8719683f1adbf1a0625d5d12126e7ac84e8f5ccd37d9058001b4636b5f1ad1c9:
- Executable file
r37/packages/trigsimp/trigsimp.tst
— 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: 4717) [annotate] [blame] [check-ins using] [more...]
- Executable file
r38/packages/trigsimp/trigsimp.tst
— 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: 4717) [annotate] [blame] [check-ins using]
% Test file for TrigSimp package %-------------------------TrigSimp-------------------------- trigsimp(tan(x+y), keepalltrig); trigsimp(ws, keepalltrig, combine); trigsimp(sin(5x-9y)); trigsimp(ws, combine); trigsimp(cos(10x), cos); trigsimp(cos(10x), sin); trigsimp((sin(x-a)+sin(x+a))/(cos(x-a)+cos(x+a))); trigsimp(cos(6x+4y), sin); trigsimp(ws, expon); trigsimp(ws, hyp); trigsimp(ws, combine); trigsimp(ws, trig, combine); trigsimp(sqrt(1-cos(2x))); trigsimp(sin(x)^20*cos(x)^20, sin); trigsimp(sin(x)^20*cos(x)^20, cos); trigsimp(sin(x)^20*cos(x)^20, compact); trigsimp(sin(x)^10, combine); trigsimp(ws, hyp); trigsimp(ws, expon); trigsimp(ws, trig); int(sin(x+y)*cos(x-y)*tan(x), x); int(trigsimp(sin(x+y)*cos(x-y)*tan(x)), x); % int(sin(x+y)*cos(x-y)/tan(x), x) hangs int(trigsimp(sin(x+y)*cos(x-y)/tan(x)), x); trigsimp(2tan(x)*(sec(x)^2 - tan(x)^2 - 1)); on rationalize; df(sqrt(1+cos(x)), x, 4); off rationalize; trigsimp(ws); df(2cos((x+y)/2)*cos((x-y)/2), x); trigsimp(ws, combine); df(int(1/cos(x), x), x); trigsimp(ws, combine); trigsimp(cos(100x)); trigsimp(ws, combine); trigsimp(sinh(3a+4b-5c)*cosh(3a-5b-6c)); trigsimp(ws, combine); trigsimp(sec(20x-y), keepalltrig); trigsimp(csc(10a-9b), keepalltrig); trigsimp(ws, combine); trigsimp(cosh(50*acosh(x))-cos(50*acos(x))); trigsimp(cos(n*acos(x))-cosh(n*acosh(x)), trig); trigsimp((2tan(log(x))*(sec(log(x))^2 - tan(log(x))^2 - 1))/x); trigsimp(sech(10x), keepalltrig); trigsimp(ws, combine); trigsimp(csch(3x-5y), keepalltrig); trigsimp(ws, combine); off precise; trigsimp((sinh(x)+cosh(x))^n+(cosh(x)-sinh(x))^n, expon); on precise; trigsimp(ws, hyp); load_package taylor; taylor(sin(x+a)*cos(x+b), x, 0, 4); trigsimp(ws, combine); %-----------------------TrigFactorize----------------------- on nopowers; % for comparison with version 2.0 trigfactorize(sin(x)**2, x); trigfactorize(1+cos(x), x); trigfactorize(1+cos(x), x/2); trigfactorize(1+cos(x), x/6); trigfactorize(sin(x)*(1-cos(x)), x); trigfactorize(sin(x)*(1-cos(x)), x/2); trigfactorize(tan(x), x); trigfactorize(sin(x*3), x); trigfactorize(sin(4x)-1, x); trigfactorize(sin(x)**4-1, x); trigfactorize(cos(x)**4-1, x); trigfactorize(sin(x)**10-cos(x)**6, x); trigfactorize(sin(x)*cos(y), x); trigfactorize(sin(2x)*cos(y)**2, y/2); trigfactorize(sin(y)**4-x**2, y); trigfactorize(sin(x), x+1); trigfactorize(sin(x), 2x); trigfactorize(sin(x)*cosh(x), x/2); trigfactorize(1+cos(2x)+2cos(x)*cosh(x), x/2); %-------------------------TrigGCD--------------------------- triggcd(sin(x), cos(x), x); triggcd(1-cos(x)^2, sin(x)^2, x); triggcd(sin(x)^4-1, cos(x)^2, x); triggcd(sin(5x+1), cos(x), x); triggcd(1-cos(2x), sin(2x), x); triggcd(-5+cos(2x)-6sin(x), -7+cos(2x)-8sin(x), x/2); triggcd(1-2cosh(x)+cosh(2x), 1+2cosh(x)+cosh(2x), x/2); triggcd(1+cos(2x)+2cos(x)*cosh(x), 1+2cos(x)*cosh(x)+cosh(2x), x/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); triggcd(sin(x)^10-1, cos(x), x); triggcd(sin(5x)+sin(3x), cos(x), x); triggcd(sin(3x)+sin(5x), sin(5x)+sin(7x), x); %----------------------------------------------------------- % New facilities in version 2 %----------------------------------------------------------- % TrigSimp applied to non-scalars data structures: trigsimp( sin(2x) = cos(2x) ); trigsimp( { sin(2x), cos(2x) } ); trigsimp( { sin(2x) = cos(2x) } ); trigsimp( mat((sin(2x),cos(2x)), (csc(2x),sec(2x))) ); % An amusing identify: trigsimp(csc x - cot x - tan(x/2)); % which could be DERIVED like this: trigsimp(csc x - cot x, x/2, tan); % A silly illustration of multiple additional trig arguments: trigsimp(csc x - cot x, x/2, x/3); % A more useful illustration of multiple additional trig arguments: trigsimp(csc x - cot x + csc y - cot y, x/2, y/2, tan); %----------------------------------------------------------- % New TrigFactorize facility: off nopowers; % REDUCE 3.7 default, gives more compact output ... trigfactorize(sin(x)^2, x); trigfactorize(1+cos(x), x); trigfactorize(1+cos(x), x/2); trigfactorize(1+cos(x), x/6); trigfactorize(sin(x)*(1-cos(x)), x); trigfactorize(sin(x)*(1-cos(x)), x/2); trigfactorize(tan(x), x); trigfactorize(sin(3x), x); trigfactorize(sin(4x) - 1, x); trigfactorize(sin(x)^4 - 1, x); trigfactorize(cos(x)^4 - 1, x); trigfactorize(sin(x)^10 - cos(x)^6, x); trigfactorize(sin(x)*cos(y), x); trigfactorize(sin(2x)*cos(y)^2, y/2); trigfactorize(sin(y)^4 - x^2, y); trigfactorize(sin(x), x+1); trigfactorize(sin(x), 2x); trigfactorize(sin(x)*cosh(x), x/2); trigfactorize(1 + cos(2x) + 2cos(x)*cosh(x), x/2); end;