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Question: Inconsistant results when using "subs"

Question:Inconsistant results when using "subs"

nugtmaple 15 Maple
integration subs
August 06 2012
0

Hi, I am solving an integration. When I use "subs" command to define the value of cl and ct, the result is inconsistant with the one when I define the cl and ct directly by using "cl:= and ct:=". (Why u1test is not equal to u2test in "Comparison #1"?) Please help

result.mw

``

> 

restart

Comparison #1

> 

assume(0 < ct, ct < cl, 0 < H, 0 < `&tau;l`, 0 < `&tau;t`, 0 < omega)
> 

NumericEventHandler(invalid_operation = `Heaviside/EventHandler`(value_at_zero = 1))
> 

``
> 

u := simplify(int(int(sin(omega*(ts+ys/ct))*Heaviside(t-ts-ys/ct), ys = H-cl*ts .. ct*ts), ts = H/(cl+ct) .. (H+cl*`&tau;l`)/(cl+ct))+int(int(sin(omega*(ts+ys/ct))*Heaviside(t-ts-ys/ct), ys = H-cl*ts .. H-cl*ts+cl*`&tau;l`), ts = (H+cl*`&tau;l`)/(cl+ct) .. (H+ct*`&tau;t`)/(cl+ct))+int(int(sin(omega*(ts+ys/ct))*Heaviside(t-ts-ys/ct), ys = ct*ts-ct*`&tau;t` .. H-cl*ts+cl*`&tau;l`), ts = (H+ct*`&tau;t`)/(cl+ct) .. (H+cl*`&tau;l`+ct*`&tau;t`)/(cl+ct)))
> 

u1test := simplify(int(int(sin(omega*(ts+(1/3140)*ys))*Heaviside(t-ts-(1/3140)*ys), ys = H-6300*ts .. 3140*ts), ts = H/(6300+3140) .. (H+6300*`&tau;l`)/(6300+3140))+int(int(sin(omega*(ts+(1/3140)*ys))*Heaviside(t-ts-(1/3140)*ys), ys = H-6300*ts .. H-6300*ts+6300*`&tau;l`), ts = (H+6300*`&tau;l`)/(6300+3140) .. (H+3140*`&tau;t`)/(6300+3140))+int(int(sin(omega*(ts+(1/3140)*ys))*Heaviside(t-ts-(1/3140)*ys), ys = 3140*ts-3140*`&tau;t` .. H-6300*ts+6300*`&tau;l`), ts = (H+3140*`&tau;t`)/(6300+3140) .. (H+6300*`&tau;l`+3140*`&tau;t`)/(6300+3140)))
> 

u2test := subs([cl = 6300, ct = 3140], u)
> 

combine(u1test-u2test)

(1/495962)*(1557816800*sin((3139/29641600)*omega*H+(3139/9440)*omega*`&tau;t`+(1/3140)*omega*t)-1557816800*Heaviside((1/9440)*H-(1/2)*t)*sin((3141/6280)*omega*t)+1557816800*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*sin((3141/6280)*omega*t)+2326124560*sin(omega*t)*Heaviside(-(1/1580)*H+`&tau;t`+(236/79)*t)-2326124560*sin(omega*t)*Heaviside(`&tau;t`-(1/1580)*H-(315/79)*`&tau;l`+(236/79)*t)+2326124560*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`-(79/236)*omega*`&tau;t`)*Heaviside(`&tau;t`-(1/1580)*H-(315/79)*`&tau;l`+(236/79)*t)-2326124560*sin((1/4720)*omega*H-(79/236)*omega*`&tau;t`)*Heaviside(-(1/1580)*H+`&tau;t`+(236/79)*t)+2326124560*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`)*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)-2326124560*sin(omega*t)*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)+778660340*sin((1/4720)*omega*H)*Heaviside(t-(1/4720)*H)-2326124560*sin(omega*t)*Heaviside(t-(1/4720)*H)-778660340*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`-(79/236)*omega*`&tau;t`)-778660340*Heaviside((1/9440)*H-(79/472)*`&tau;t`-(1/2)*t)*sin((1/4720)*omega*H-(79/236)*omega*`&tau;t`)+778660340*Heaviside((1/9440)*H-(79/472)*`&tau;t`-(1/2)*t)*sin(omega*t)+778660340*Heaviside(-(1/2)*t+(1/9440)*H+(315/472)*`&tau;l`-(79/472)*`&tau;t`)*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`-(79/236)*omega*`&tau;t`)-778660340*Heaviside(-(1/2)*t+(1/9440)*H+(315/472)*`&tau;l`-(79/472)*`&tau;t`)*sin(omega*t)+2326124560*sin(omega*t)-2326124560*cos(omega*t)*t*omega-1547464220*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`)+778660340*sin((1/4720)*omega*H-(79/236)*omega*`&tau;t`)-1557816800*sin((3139/29641600)*omega*H+(197757/296416)*omega*`&tau;l`+(3139/9440)*omega*`&tau;t`+(1/3140)*omega*t)+1557816800*sin((3139/29641600)*omega*H+(197757/296416)*omega*`&tau;l`+(1/3140)*omega*t)-1557816800*sin((3139/29641600)*omega*H+(1/3140)*omega*t)-778660340*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`)+1557816800*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`)*sin((3139/9859600)*omega*H+(197757/98596)*omega*`&tau;l`-(1569/1570)*omega*t)+1547464220*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`)*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`)+1547464220*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`)*sin((1/492980)*omega*H+(315/24649)*omega*`&tau;l`-(158/157)*omega*t)+1557816800*Heaviside(t-(1/4720)*H+(79/236)*`&tau;t`)*sin(-(1569/1570)*omega*t+(3139/9859600)*omega*H)-1557816800*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`)*sin((3139/29641600)*omega*H+(197757/296416)*omega*`&tau;l`+(1/3140)*omega*t)+1557816800*Heaviside((1/9440)*H-(79/472)*`&tau;t`-(1/2)*t)*sin((3141/6280)*omega*t+(3139/6280)*omega*`&tau;t`)-1557816800*Heaviside(t-(1/4720)*H+(79/236)*`&tau;t`)*sin((3139/29641600)*omega*H+(3139/9440)*omega*`&tau;t`+(1/3140)*omega*t)-1557816800*Heaviside((1/9440)*H-(79/472)*`&tau;t`-(1/2)*t)*sin((3139/29641600)*omega*H+(3139/9440)*omega*`&tau;t`+(1/3140)*omega*t)+1557816800*Heaviside(-(1/2)*t+(1/9440)*H+(315/472)*`&tau;l`-(79/472)*`&tau;t`)*sin((3139/29641600)*omega*H+(197757/296416)*omega*`&tau;l`+(3139/9440)*omega*`&tau;t`+(1/3140)*omega*t)-1557816800*Heaviside(-(1/2)*t+(1/9440)*H+(315/472)*`&tau;l`-(79/472)*`&tau;t`)*sin((3141/6280)*omega*t+(3139/6280)*omega*`&tau;t`)-1557816800*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`+(79/236)*`&tau;t`)*sin((3139/9859600)*omega*H+(197757/98596)*omega*`&tau;l`-(1569/1570)*omega*t)+1547464220*Heaviside(t-(1/4720)*H+(79/236)*`&tau;t`)*sin(-(158/157)*omega*t+(1/492980)*omega*H)+1557816800*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`+(79/236)*`&tau;t`)*sin((3139/29641600)*omega*H+(197757/296416)*omega*`&tau;l`+(3139/9440)*omega*`&tau;t`+(1/3140)*omega*t)-1557816800*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*sin((3139/29641600)*omega*H+(197757/296416)*omega*`&tau;l`+(1/3140)*omega*t)+1547464220*Heaviside(t-(1/4720)*H+(79/236)*`&tau;t`)*sin((1/4720)*omega*H-(79/236)*omega*`&tau;t`)+1557816800*Heaviside(t-(1/4720)*H)*sin((3139/29641600)*omega*H+(1/3140)*omega*t)-1557816800*Heaviside(t-(1/4720)*H)*sin(-(1569/1570)*omega*t+(3139/9859600)*omega*H)-1547464220*Heaviside(t-(1/4720)*H)*sin(-(158/157)*omega*t+(1/492980)*omega*H)-1547464220*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`+(79/236)*`&tau;t`)*sin((1/492980)*omega*H+(315/24649)*omega*`&tau;l`-(158/157)*omega*t)+1557816800*Heaviside((1/9440)*H-(1/2)*t)*sin((3139/29641600)*omega*H+(1/3140)*omega*t)-1547464220*Heaviside(t-(1/4720)*H-(315/236)*`&tau;l`+(79/236)*`&tau;t`)*sin((1/4720)*omega*H+(315/236)*omega*`&tau;l`-(79/236)*omega*`&tau;t`)+492823*cos(omega*t)*H*Heaviside(-(1/1580)*H+`&tau;t`+(236/79)*t)*omega-3104784900*cos(omega*t)*`&tau;l`*Heaviside(`&tau;t`-(1/1580)*H-(315/79)*`&tau;l`+(236/79)*t)*omega+778660340*cos(omega*t)*`&tau;t`*Heaviside(`&tau;t`-(1/1580)*H-(315/79)*`&tau;l`+(236/79)*t)*omega+2326124560*cos(omega*t)*t*Heaviside(`&tau;t`-(1/1580)*H-(315/79)*`&tau;l`+(236/79)*t)*omega-492823*cos(omega*t)*H*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)*omega-3104784900*cos(omega*t)*`&tau;l`*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)*omega+2326124560*cos(omega*t)*t*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)*omega-492823*cos(omega*t)*H*Heaviside(t-(1/4720)*H)*omega+2326124560*cos(omega*t)*t*Heaviside(t-(1/4720)*H)*omega-492823*cos(omega*t)*H*Heaviside(`&tau;t`-(1/1580)*H-(315/79)*`&tau;l`+(236/79)*t)*omega-778660340*cos(omega*t)*`&tau;t`*Heaviside(-(1/1580)*H+`&tau;t`+(236/79)*t)*omega-2326124560*cos(omega*t)*t*Heaviside(-(1/1580)*H+`&tau;t`+(236/79)*t)*omega+778660340*Heaviside((1/9440)*H-(1/2)*t)*sin((1/4720)*omega*H)-778660340*Heaviside((1/9440)*H-(1/2)*t)*sin(omega*t)+778660340*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*sin(omega*t)-778660340*sin((1/4720)*omega*H)+492823*cos(omega*t)*omega*H+3104784900*cos(omega*t)*omega*`&tau;l`)/omega^2

 (1)
> 

``

 

Comparison#2

> 

restart
> 

assume(0 < ct, ct < cl, 0 < H, 0 < `&tau;l`, 0 < `&tau;t`, 0 < omega)
> 

NumericEventHandler(invalid_operation = `Heaviside/EventHandler`(value_at_zero = 1)):
> 

``
> 

cl := 6300:
> 

ct := 3140:
> 

u := simplify(int(int(sin(omega*(ts+ys/ct))*Heaviside(t-ts-ys/ct), ys = H-cl*ts .. ct*ts), ts = H/(cl+ct) .. (H+cl*`&tau;l`)/(cl+ct))+int(int(sin(omega*(ts+ys/ct))*Heaviside(t-ts-ys/ct), ys = H-cl*ts .. H-cl*ts+cl*`&tau;l`), ts = (H+cl*`&tau;l`)/(cl+ct) .. (H+ct*`&tau;t`)/(cl+ct))+int(int(sin(omega*(ts+ys/ct))*Heaviside(t-ts-ys/ct), ys = ct*ts-ct*`&tau;t` .. H-cl*ts+cl*`&tau;l`), ts = (H+ct*`&tau;t`)/(cl+ct) .. (H+cl*`&tau;l`+ct*`&tau;t`)/(cl+ct))):
> 

u1test := simplify(int(int(sin(omega*(ts+(1/3140)*ys))*Heaviside(t-ts-(1/3140)*ys), ys = H-6300*ts .. 3140*ts), ts = H/(6300+3140) .. (H+6300*`&tau;l`)/(6300+3140))+int(int(sin(omega*(ts+(1/3140)*ys))*Heaviside(t-ts-(1/3140)*ys), ys = H-6300*ts .. H-6300*ts+6300*`&tau;l`), ts = (H+6300*`&tau;l`)/(6300+3140) .. (H+3140*`&tau;t`)/(6300+3140))+int(int(sin(omega*(ts+(1/3140)*ys))*Heaviside(t-ts-(1/3140)*ys), ys = 3140*ts-3140*`&tau;t` .. H-6300*ts+6300*`&tau;l`), ts = (H+3140*`&tau;t`)/(6300+3140) .. (H+6300*`&tau;l`+3140*`&tau;t`)/(6300+3140))):
> 

u2test := subs([cl = 6300, ct = 3140], u):
> 

combine(u1test-u2test)

0

 (2)
> 

``


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