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.

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, $\mathrm{\_V}$ is used.

You can use these commands as a functional argument to collect, replacing complicated coefficients in a sum of terms by simple labels.

The protected variable LastUsed contains a table of indices pointing to the last used label index in each variable.

$\mathrm{with}\left(\mathrm{LargeExpressions}\right)\:$

$p≔\mathrm{randpoly}\left(\left[x\,y\,z\right]\,\mathrm{degree}=5\,\mathrm{dense}\right)$

$p≔-7x^5+22x^{4}y-55x^{4}z+87x^3{y}^2-56x^{3}yz-62x^3{z}^2-4x^2{y}^3-83x^2{y}^{2}z+62x^{2}y{z}^2-44x^2{z}^3-10x{y}^4-7x{y}^{3}z+42x{y}^2{z}^2+75xy{z}^3+72x{z}^4+29y^5+98y^{4}z+10y^3{z}^2-29y^2{z}^3-47y{z}^4-10z^5-94x^4+97x^{3}z-10x^2{y}^2-82x^{2}yz+71x^2{z}^2-40x{y}^3-50x{y}^{2}z-92xy{z}^2+37x{z}^3-23y^4-61y^{3}z+95y^2{z}^2+40y{z}^3+31z^4-73x^3+80x^{2}y-17x^{2}z+23x{y}^2+6xyz-23x{z}^2-8y^3+11y^{2}z-81y{z}^2-51z^3-75x^2+74xy+87xz-49y^2+91yz+77z^2+44x+68y+95z+1$

$\mathrm{compact}≔\mathrm{collect}\left(p\,z\,\mathrm{Veil}\left[K\right]\right)$

$\mathrm{compact}≔-10z^5+K_1{z}^4-K_2{z}^3-K_3{z}^2-K_{4}z-K_5$

$\mathrm{zero}≔\mathrm{normal}\left(\mathrm{Unveil}\left[K\right]\left(\mathrm{compact}\,\mathrm{\infty }\right)-p\right)$

$\mathrm{zero}≔0$

$\mathrm{compact2}≔\mathrm{collect}\left(p\,y\,\mathrm{Veil}\left[C\right]\right)$

$\mathrm{compact2}≔29y^5-C_1{y}^4-C_2{y}^3+C_3{y}^2+C_{4}y-C_5$

$\mathrm{CS}≔\left[\mathrm{seq}\left(C\left[i\right]=\mathrm{Unveil}\left[C\right]\left(C\left[i\right]\right)\,i=1..\mathrm{LastUsed}\left[C\right]\right)\right]$

$\mathrm{CS}≔\left[C_1=10x-98z+23\,C_2=4x^2+7xz-10z^2+40x+61z+8\,C_3=87x^3-83x^{2}z+42x{z}^2-29z^3-10x^2-50xz+95z^2+23x+11z-49\,C_4=22x^4-56x^{3}z+62x^2{z}^2+75x{z}^3-47z^4-82x^{2}z-92x{z}^2+40z^3+80x^2+6xz-81z^2+74x+91z+68\,C_5=7x^5+55x^{4}z+62x^3{z}^2+44x^2{z}^3-72x{z}^4+10z^5+94x^4-97x^{3}z-71x^2{z}^2-37x{z}^3-31z^4+73x^3+17x^{2}z+23x{z}^2+51z^3+75x^2-87xz-77z^2-44x-95z-1\right]$

$\mathrm{CodeGeneration}\left[\mathrm{Fortran}\right]\left(\mathrm{CS}\right)$

      C(1) = 10 * x - 98 * z + 23
      C(2) = 4 * x ** 2 + 7 * x * z - 10 * z ** 2 + 40 * x + 61 * z + 8
      C(3) = 87 * x ** 3 - 83 * x ** 2 * z + 42 * x * z ** 2 - 29 * z **
     # 3 - 10 * x ** 2 - 50 * x * z + 95 * z ** 2 + 23 * x + 11 * z - 49
      C(4) = 22 * x ** 4 - 56 * x ** 3 * z + 62 * x ** 2 * z ** 2 + 75 *
     # x * z ** 3 - 47 * z ** 4 - 82 * x ** 2 * z - 92 * x * z ** 2 + 40
     # * z ** 3 + 80 * x ** 2 + 6 * x * z - 81 * z ** 2 + 74 * x + 91 *
     #z + 68
      C(5) = 7 * x ** 5 + 55 * x ** 4 * z + 62 * x ** 3 * z ** 2 + 44 *
     #x ** 2 * z ** 3 - 72 * x * z ** 4 + 10 * z ** 5 + 94 * x ** 4 - 97
     # * x ** 3 * z - 71 * x ** 2 * z ** 2 - 37 * x * z ** 3 - 31 * z **
     # 4 + 73 * x ** 3 + 17 * x ** 2 * z + 23 * x * z ** 2 + 51 * z ** 3
     # + 75 * x ** 2 - 87 * x * z - 77 * z ** 2 - 44 * x - 95 * z - 1

$\mathrm{de}≔\sin \left(x\right)\mathrm{diff}\left(y\left(x\right)\,x\,x\right)-2\cos \left(x\right)\mathrm{diff}\left(y\left(x\right)\,x\right)-a\sin \left(x\right)y\left(x\right)$

$\mathrm{de}≔\sin \left(x\right)\left(\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)\right)-2\cos \left(x\right)\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)-a\sin \left(x\right)y\left(x\right)$

$\mathrm{Order}≔14$

$\mathrm{Order}≔14$

$\mathrm{soln}≔\mathrm{dsolve}\left(\left\{\mathrm{de}\right\}\,y\left(x\right)\,'\mathrm{series}'\right)\:$

$\mathrm{algsol}≔\mathrm{convert}\left(\mathrm{eval}\left(y\left(x\right)\,\mathrm{soln}\right)\,\mathrm{polynom}\right)\:$

$\mathrm{collect}\left(\mathrm{algsol}\,x\,\mathrm{Veil}\left[L\right]\right)$

$\frac{1}{217945728000}{L}_1{x}^{15}+\frac{1}{518918400}{L}_2{x}^{13}-\frac{1}{39916800}{L}_3{x}^{12}+\frac{1}{6652800}{L}_4{x}^{11}-\frac{1}{302400}{L}_5{x}^{10}+\frac{1}{15120}{L}_6{x}^9-\frac{1}{3360}{L}_7{x}^8+\frac{1}{840}{L}_8{x}^7-\frac{1}{60}{L}_9{x}^6+\frac{1}{10}{L}_{10}{x}^5-\frac{1}{2}{L}_{11}{x}^4+\mathrm{c\_\_1}{x}^3-6L_{12}{x}^2+12\mathrm{c\_\_2}$

$\mathrm{seq}\left(L\left[k\right]=\mathrm{Unveil}\left[L\right]\left(L\left[k\right]\right)\,k=1..\mathrm{LastUsed}\left[L\right]\right)$

$L_1=\mathrm{c\_\_1}\left(7a^6-224a^5+2016a^4-7680a^3+14080a^2-12288a+4096\right),L_2=\mathrm{c\_\_1}\left(3a^5-70a^4+448a^3-1152a^2+1280a-512\right),L_3=\mathrm{c\_\_2}a\left(11a^5-220a^4+1232a^3-2816a^2+2816a-1024\right),L_4=\mathrm{c\_\_1}\left(5a^4-80a^3+336a^2-512a+256\right),L_5=\mathrm{c\_\_2}a\left(9a^4-120a^3+432a^2-576a+256\right),L_6=\mathrm{c\_\_1}\left(a^3-10a^2+24a-16\right),L_7=\mathrm{c\_\_2}a\left(7a^3-56a^2+112a-64\right),L_8=\mathrm{c\_\_1}\left(3a^2-16a+16\right),L_9=\mathrm{c\_\_2}a\left(5a^2-20a+16\right),L_{10}=\mathrm{c\_\_1}\left(a-2\right),L_{11}=\mathrm{c\_\_2}a\left(3a-4\right),L_{12}=\mathrm{c\_\_2}a$

Corless, Robert M. Essential Maple 7. Springer-Verlag.