LargeExpressions[Veil] - hide a complicated expression
LargeExpressions[Unveil] - show a hidden complicated expression
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Calling Sequence
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Veil[K]( complicated_expression )
Unveil[K]( expressions_with_Ks, n )
LastUsed
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Parameters
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K
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unassigned name to use as a label
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complicated_expression
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expression
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expressions_with_Ks
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expression that has been veiled
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n
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positive integer representing the level of unveiling, or infinity, meaning all levels
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Description
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During a long calculation, it is sometimes useful to explicitly control Maple evaluation of expressions by hiding their values under user-defined labels. This allows compact representation of the results as a computation sequence, generated from the natural hierarchy of the problem.
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The Veil command is used to hide information, Unveil to reveal the hidden information. Both commands take an index that specifies the label to use; multiple labels can be present in an expression and manipulated independently. If no label is specified, is used.
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You can use these commands as a functional argument to collect, replacing complicated coefficients in a sum of terms by simple labels.
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The protected variable LastUsed contains a table of indices pointing to the last used label index in each variable.
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Examples
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Treat a polynomial in as a polynomial in with hidden coefficients depending on .
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Create another sequence using different labels. Note that the table of last used indices is keyed by the label name (in this case C).
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![CS := [C[1] = 10*x+23-98*z, C[2] = 40*x-10*z^2+7*x*z+61*z+4*x^2+8, C[3] = 23*x-83*x^2*z-29*z^3+95*z^2-50*x*z+87*x^3+11*z-10*x^2-49+42*x*z^2, C[4] = 40*z^3-92*x*z^2-47*z^4+75*x*z^3+6*x*z+91*z-56*x^3*z+68+22*x^4+62*x^2*z^2-81*z^2+74*x+80*x^2-82*x^2*z, C[5] = -1-44*x+44*x^2*z^3-95*z+10*z^5+51*z^3-77*z^2+73*x^3+55*x^4*z+7*x^5+75*x^2+62*x^3*z^2-31*z^4+17*x^2*z+94*x^4-87*x*z-71*x^2*z^2-72*x*z^4-37*x*z^3+23*x*z^2-97*x^3*z]](/support/helpjp/helpview.aspx?si=9252/file02016/math147.png)
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C(1) = 10 * x + 23 - 98 * z
C(2) = 40 * x - 10 * z ** 2 + 7 * x * z + 61 * z + 4 * x ** 2 + 8
C(3) = 23 * x - 83 * x ** 2 * z - 29 * z ** 3 + 95 * z ** 2 - 50 *
# x * z + 87 * x ** 3 + 11 * z - 10 * x ** 2 - 49 + 42 * x * z ** 2
C(4) = 40 * z ** 3 - 92 * x * z ** 2 - 47 * z ** 4 + 75 * x * z **
# 3 + 6 * x * z + 91 * z - 56 * x ** 3 * z + 68 + 22 * x ** 4 + 62
#* x ** 2 * z ** 2 - 81 * z ** 2 + 74 * x + 80 * x ** 2 - 82 * x **
# 2 * z
C(5) = -1 - 44 * x + 44 * x ** 2 * z ** 3 - 95 * z + 10 * z ** 5 +
# 51 * z ** 3 - 77 * z ** 2 + 73 * x ** 3 + 55 * x ** 4 * z + 7 * x
# ** 5 + 75 * x ** 2 + 62 * x ** 3 * z ** 2 - 31 * z ** 4 + 17 * x
#** 2 * z + 94 * x ** 4 - 87 * x * z - 71 * x ** 2 * z ** 2 - 72 *
#x * z ** 4 - 37 * x * z ** 3 + 23 * x * z ** 2 - 97 * x ** 3 * z
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The following Frobenius series solution to a differential equation has complicated coefficients, which obscure the structure of the solution.
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![(1/217945728000)*L[1]*x^15+(1/518918400)*L[2]*x^13-(1/39916800)*L[3]*x^12+(1/6652800)*L[4]*x^11-(1/302400)*L[5]*x^10+(1/15120)*L[6]*x^9-(1/3360)*L[7]*x^8+(1/840)*L[8]*x^7-(1/60)*L[9]*x^6+(1/10)*L[10]*x^5-(1/2)*L[11]*x^4+_C1*x^3-6*L[12]*x^2+12*_C2](/support/helpjp/helpview.aspx?si=9252/file02016/math197.png)
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![L[1] = _C1*(4096-12288*a+14080*a^2+2016*a^4-7680*a^3-224*a^5+7*a^6), L[2] = _C1*(-512+1280*a-1152*a^2-70*a^4+448*a^3+3*a^5), L[3] = _C2*a*(-1024+1232*a^3-2816*a^2-220*a^4+11*a^5+2816*a), L[4] = _C1*(256-512*a+336*a^2-80*a^3+5*a^4), L[5] = _C2*a*(256+432*a^2-120*a^3+9*a^4-576*a), L[6] = _C1*(-16+24*a-10*a^2+a^3), L[7] = _C2*a*(-56*a^2+7*a^3-64+112*a), L[8] = _C1*(16-16*a+3*a^2), L[9] = _C2*a*(-20*a+5*a^2+16), L[10] = _C1*(a-2), L[11] = _C2*a*(-4+3*a), L[12] = _C2*a](/support/helpjp/helpview.aspx?si=9252/file02016/math204.png)
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Example based on content provided in Chapter 2 of Essential Maple 7.
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References
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Corless, Robert M. Essential Maple 7. Springer-Verlag.
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