Subject: Maxima: trigsimp() in Maxima 5.12 v 5.10/5.9.1
From: C. Frangos
Date: Mon, 23 Jul 2007 23:40:26 +0200
20 July 2007
For the application below, the function trigsimp() seems to be behave
differently in Maxima 5.12 versus Maxima 5.10/5.9.1.
Any assistance with the following would be appreciated:
(1) The function trigsimp() is applied to the expression y1 below and
different results are obtained:
Maxima5.12
(%i2) y1:sqrt(sin(delta3)^2*Lc^2/(2*sin(delta3)*Lo1+cos(delta3)*Lc)^2+1);
(%o2) sqrt(sin(delta3)^2*Lc^2/(2*sin(delta3)*Lo1+cos(delta3)*Lc)^2+1)
(%i3) trigsimp(y1);
(%o3) sqrt(4*sin(delta3)^2*Lo1^2+4*cos(delta3)*sin(delta3)*Lc*Lo1+Lc^2)
/sqrt(4*sin(delta3)^2*Lo1^2+4*cos(delta3)*sin(delta3)*Lc*Lo1
+cos(delta3)^2*Lc^2)
Maxima5.10
(%i4) y1;
(%o4) sqrt(sin(delta3)^2*Lc^2/(2*sin(delta3)*Lo1+cos(delta3)*Lc)^2+1)
(%i5) trigsimp(y1);
(%o5) sqrt(4*sin(delta3)^2*Lo1^2+4*cos(delta3)*sin(delta3)*Lc*Lo1+Lc^2)
/(2*sin(delta3)*Lo1+cos(delta3)*Lc)
Maxima5.9.1
(%i133) y1:sqrt(sin(delta3)^2*Lc^2/(2*sin(delta3)*Lo1+cos(delta3)*Lc)^2+1);
(%o133) SQRT(SIN(delta3)^2*LC^2/(2*SIN(delta3)*Lo1+COS(delta3)*LC)^2+1)
(%i134) trigsimp(y1);
(%o134) SQRT(4*SIN(delta3)^2*Lo1^2+4*COS(delta3)*SIN(delta3)*LC*Lo1+LC^2)
/(2*SIN(delta3)*Lo1+COS(delta3)*LC)
(2) It appears that in Maxima 5.10/5.9.1, trigsimp() assumes that expres1 =
2*sin(delta3)*Lo1+cos(delta3)*Lc > 0 in y1.
It then simplifies sqrt(expres1^2) to expres1.
In Maxima 5.12, trigsimp() does not do this.
(3) For this application, the assumption expres1 > 0 is physically correct.
What is the Maxima command to implement this assumption explicitly ?
Thanks very much.
Regards,
C. Frangos.