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- "== Equations System Solving by Substitution == SUBST.DMO = 30.03.00"
- "Multiple Solutions Supported. Copyright (C) 2000 by S.V.Biryukov"
- " Email: ciprel@cityline.ru Subject: DERIVE"
- " uses SUBST.MTH. For DERIVE v.5.00 & later. See SUBST.DOC "
- " "
- "SOLVE_(m,v):=solves matrix of eq. m for variables v by substitution"
- " m - 1 column matrix of equations, "
- " v - vector (or 1 col. matrix) of solve variables. "
- " Eq. & variables order in m & v define substitution order"
- " Use ONLY in EXACT mode !!! "
- " ******* Use SOLVE_() function ONLY in EXACT Mode !!! ************"
- LOAD(["subst.mth","..\users\subst.mth"])
- " SOLVE_() can solve simple nonlinear eq. systems by substitution. "
- SOLVE_([[c=a/b],[b-1=c],[2*c=a-2]],[a,b,c])=
- "One column matrix of variables is also supported. "
- SOLVE_([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]])=
- "Other variables (& thus substitutions) order, but the same solution"
- SOLVE_([[c=a/b],[b-1=c],[2*c=a-2]],[[b],[c],[a]])=
- "APPEND(RHS()) combination returns a vector of variables' values. "
- APPEND(RHS([[a=6],[b=3],[c=2]]))=
- "You can use SBST() to test solutions. SBST(u,x,x0) substitutes x=x0"
- "in u. x & x0 - vectors or 1 column matrices of variables & values. "
- SBST([[c=a/b],[b-1=c],[2*c=a-2]],[b;c;a],[3;2;6])=
- "Linear eq. systems. can be also solved "
- SOLVE_([[2*a+3*b+4*c=12],[4*a+5*b-7*c=-7],[9*a+4*b+3*c=14.5]],[[a],[b],[c]])=
- "=================== Inside the Utility ====================== "
-
- "Forward substitutions. A tree of solutions & reduced eq. systems. "
- SOLF([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]])
-
- "Forward substitutions. A part of a tree for 2 first variables. "
- SOLF([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]],2)
-
- "2 solution vectors returned by forward/back substitutions "
- SOLB(SOLF([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]]))=
-
- "1st vector test. Substitute it in the eq. system. NOT a Solution!"
- SBST([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]],[[0],[0],[-1]])=
-
- "2nd vector test. Valid Solution ! "
- SBST([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]],[[6],[3],[2]])=
-
- "SOLVE_() returns only valid solutions. "
- SOLVE_([[c=a/b],[b-1=c],[2*c=a-2]],[[a],[b],[c]])=
- "****** Use SOLVE_() function ONLY in EXACT Mode !!! *************"
- " "
- ".................................................................."
- " Additional Information is in SUBST.DOC "
- ".................................................................."
- "======================== SUBST.DMO END ========================"
-