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Question: Why does this elliptic integral not simplify with indexed names

Question:Why does this elliptic integral not simplify with indexed names

C_R 3447 Maple
integration elliptic-integral indexed
2 hours ago
0

NULL

Evaluation with `ϕ__0`subscripted

-t(0)+t(`ϕ`(t)) = Int(1/sqrt(2*C*cos(`ϕ`)-2*C*cos(`ϕ__0`)), `ϕ` = 0 .. `ϕ`(t), continuous)

-t(0)+t(varphi(t)) = Int(1/(2*C*cos(varphi)-2*C*cos(varphi__0))^(1/2), varphi = 0 .. varphi(t), continuous)

 (1)

t(0) = 0, `ϕ`(t) = `ϕ__0`, t(`ϕ__0`) = (1/4)*T

t(0) = 0, varphi(t) = varphi__0, t(varphi__0) = (1/4)*T

 (2)

subs(t(0) = 0, varphi(t) = varphi__0, t(varphi__0) = (1/4)*T, -t(0)+t(varphi(t)) = Int(1/(2*C*cos(varphi)-2*C*cos(varphi__0))^(1/2), varphi = 0 .. varphi(t), continuous))

(1/4)*T = Int(1/(2*C*cos(varphi)-2*C*cos(varphi__0))^(1/2), varphi = 0 .. varphi__0, continuous)

 (3)

isolate(`assuming`([simplify(value((1/4)*T = Int(1/(2*C*cos(varphi)-2*C*cos(varphi__0))^(1/2), varphi = 0 .. varphi__0, continuous)))], [C > 0, 0 < `&varphi;__0` and `&varphi;__0` < Pi]), T)

T = 4*InverseJacobiAM((1/2)*varphi__0, csc((1/2)*varphi__0))*csc((1/2)*varphi__0)/C^(1/2)

 (4)

NULL

NULL

Replacing now in the above varphi__0 by varphi[0]

NULL

Evaluation with `&varphi;`[0] indexed

-t(0)+t(`&varphi;`(t)) = Int(1/sqrt(2*C*cos(`&varphi;`)-2*C*cos(`&varphi;`[0])), `&varphi;` = 0 .. `&varphi;`(t), continuous)

-t(0)+t(varphi(t)) = Int(1/(2*C*cos(varphi)-2*C*cos(varphi[0]))^(1/2), varphi = 0 .. varphi(t), continuous)

 (5)

t(0) = 0, `&varphi;`(t) = `&varphi;`[0], t(`&varphi;`[0]) = (1/4)*T

t(0) = 0, varphi(t) = varphi[0], t(varphi[0]) = (1/4)*T

 (6)

subs(t(0) = 0, varphi(t) = varphi[0], t(varphi[0]) = (1/4)*T, -t(0)+t(varphi(t)) = Int(1/(2*C*cos(varphi)-2*C*cos(varphi[0]))^(1/2), varphi = 0 .. varphi(t), continuous))

(1/4)*T = Int(1/(2*C*cos(varphi)-2*C*cos(varphi[0]))^(1/2), varphi = 0 .. varphi[0], continuous)

 (7)

isolate(`assuming`([simplify(value((1/4)*T = Int(1/(2*C*cos(varphi)-2*C*cos(varphi[0]))^(1/2), varphi = 0 .. varphi[0], continuous)))], [C > 0, 0 < `&varphi;`[0] and `&varphi;`[0] < Pi]), T)

T = 4*2^(1/2)*(-(limit(((-cos(varphi)+cos(varphi[0]))/(-1+cos(varphi[0])))^(1/2)*InverseJacobiAM((1/2)*varphi, csgn(sin((1/2)*varphi[0]))*csc((1/2)*varphi[0]))/(cos(varphi)-cos(varphi[0]))^(1/2), varphi = 0, right))*(cos(varphi[0])-cos(varphi[0][0]))^(1/2)+((-cos(varphi[0])+cos(varphi[0][0]))/(-1+cos(varphi[0][0])))^(1/2)*InverseJacobiAM((1/2)*varphi[0], csgn(sin((1/2)*varphi[0][0]))*csc((1/2)*varphi[0][0])))/(C^(1/2)*(cos(varphi[0])-cos(varphi[0][0]))^(1/2))

 (8)

NULL


The double indices in the above limit do not make sense.

In case this is a bug: Is there any workaround for indexed names? I want to use them to have numbers in indices in roman which seems to be not possible with subscripts. 

 

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