[MUG] simplify or subs

[MUG] Re: simplify or subs
Author: Maple Group    Posted: 24/11/2000 14:22:41 GMT
>> From: Maple Group -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 20 Nov 2000 13:08:51 -0500 To: From: "Gerald A. Edgar" Subject: simplify or subs zxl wrote: > >[>`E`:=y^2 = x^3+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2; > >i want a[1]^2+4*a[2] replace by b[2]; >2*a[4]+a[1]*a[3] replace by b[4] and >a[3]^4+4*a[6] by b[6] a[3]^4 here does not match a[3]^2 in E. I assume below you mean a[3]^2. > >i mean >b[2]:=a[1]^2+4*a[2]; >b[4]:=2*a[4]+a[1]*a[3]; >b[6]:=a[3]^4+4*a[6]; > >but >[>subs({a[1]^2+4*a[2]=b[2],2*a[4]+a[1]*a[3]=b[4],a[3]^4+4*a[6]=b[6]},`E`); >doesn't work. > Using a bit of user input, here is what I came up with: > E:=y^2 = x^3+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2; 2 3 2 2 E := y = x + (1/4 a[1] + a[2]) x + (1/2 a[1] a[3] + a[4]) x 2 + a[6] + 1/4 a[3] > eqns := {a[1]^2+4*a[2]=b[2], > 2*a[4]+a[1]*a[3]=b[4], > a[3]^2+4*a[6]=b[6]}; 2 eqns := {a[3] + 4 a[6] = b[6], 2 a[4] + a[1] a[3] = b[4], 2 a[1] + 4 a[2] = b[2]} > eqns2 := solve(eqns,{a[2],a[4],a[6]}); 2 eqns2 := {a[2] = - 1/4 a[1] + 1/4 b[2], 2 a[6] = - 1/4 a[3] + 1/4 b[6], a[4] = - 1/2 a[1] a[3] + 1/2 b[4]} > eval(E,eqns2); 2 3 2 y = x + 1/4 b[2] x + 1/2 b[4] x + 1/4 b[6] The user input was choosing which three of the a's to solve for. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 21 Nov 2000 00:27:53 -0500 From: "Douglas B. Meade" To: Subject: simplify or subs Dear MUG: I recently responded to a similar question on the Maple newsgroup. But, here is a similarly worded response in this forum. You can oftentimes achieve your desired goal by using the algsubs command (see ?algsubs for a full description). However, there are many occasions when algsubs is not sufficient. In those cases it is frequently beneficial to introduce an artificial parameter for the expression of interest and to proceed as follows: > F2 := subs( a[2]=(b[2]-a[1]^2)/4, F ); > F3 := simplify( F2 ); If you would like to see F expressed in terms of a[1]^2+4*a[2] (instead of b[2]), add the command: > F4 := subs( b[2]=a[1]^2+4*a[2], F3 ); I hope this helps, Doug -------------------------------------------------------------------------- Douglas B. Meade Phone: (803) 777-6183 FAX: (803) 777-6527 Department of Mathematics E-mail: USC, Columbia, SC 29208 URL: http://www.math.sc.edu/~meade/ -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Colin Birch" To: Date: Tue, 21 Nov 2000 11:13:55 +0000 Subject: simplify or subs This seems to be a frequent problem in Maple. A common problem with subs() is the temptation to ask Maple to replace expressions rather than variables. Replacing expressions only works in very simple cases. Often the successful approach is to reverse the substitution equations by simply using solve(). Try this. I have changed your equation for b[6], because I think you had a typo. > restart; > eqn1:=b[2]=a[1]^2+4*a[2]; > eqn2:=b[4]=2*a[4]+a[1]*a[3]; > eqn3:=b[6]=a[3]^2+4*a[6]; > sol1:=solve({eqn1,eqn2,eqn3},{a[1],a[2],a[3],a[4],a[6]}); 2 sol1 := {a[2] = 1/4 b[2] - 1/4 a[1] , a[4] = 1/2 b[4] - 1/2 a[1] a[3], a[6] = 1/4 b[6] - 1/4 a[3] , a[1] = a[1], a[3] = a[3]} > E:=y^2 = > x^3+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2; > subs(sol1,E); 2 3 2 y = x + 1/4 b[2] x + 1/2 b[4] x + 1/4 b[6] QED. -------------------------------------------------------------------------- Colin Birch Plant Ecology and Community Dynamics Programme, MLURI, Craigiebuckler, Aberdeen, AB15 8QH, UK E-mail: Tel/Fax: +44 1224 318611/311556 -------------------------------------------------------------------------- -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 21 Nov 2000 07:34:35 -0600 From: Herman Jaramillo To: Subject: simplify or subs First of all, I believe that in b[6] you want a[3]^2+4*a[6]=b[6] #note that a[3] should be to the second power Next instruction does what you want. subs({a[1]^2/4+a[2]=b[2]/4,a[4]+a[1]*a[3]/2=b[4]/2,a[3]^2/4+a[6]=b[6]/4},`E`); Regards. Herman. -- Herman Jaramillo phone: 713-689-6503 Research Geophysicist fax : 713-689-6100 Baker Hughes (Western Geophysical) email: 3600 Briarpark Drive (77042-5275) P.O. Box 2469 Houston, Texas 77252-2469 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Symancyk, Daniel" To: Subject: simplify or subs Date: Tue, 21 Nov 2000 13:44:37 -0500 subs does not work because it performs substitutions only on operands of the original expression. Use algsubs instead. Note that I've changed the exponent in the third substitution to make it consistent with the original E. The following should do what you want. > E:=y^2 = x^3+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2; > F:=algsubs(a[1]^2+4*a[2]=b[2],E); > G:=algsubs(2*a[4]+a[1]*a[3]=b[4],F); > H:=algsubs(a[3]^2+4*a[6]=b[6],G); Dan Symancyk Department of Mathematics Anne Arundel Community College Arnold, MD 21012 410-541-2587 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Wed, 22 Nov 2000 12:58:02 +0900 To: From: tanaka Subject: simplify or subs In this case, we should not use "subs", but "simplify". Try the followings; >`E`:=y^2 = x^3+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2; >siderule1:=a[1]^2+4*a[2]=b[2]; siderule2:=2*a[4]+a[1]*a[3]=b[4]; siderule3:=a[3]^2+4*a[6]=b[6]; >simplify(`E`,{siderule1,siderule2,siderule3}); And if the descending powers in x is expected, evaluate the following procedure; >sort(%,[x]); We finally have y^2 = x^3+1/4*b[2]*x^2+1/2*b[4]*x+1/4*b[6] -------------------------------------------------------------------- Dr.TANAKA, Kazuo, Canon Inc., Tokyo, Japan -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Wed, 22 Nov 2000 11:30:26 +0100 (CET) From: To: Subject: simplify or subs In the online help of `algsubs' you can find : The function algsubs performs an algebraic substitution, replacing occurrences of a with b in the expression f. It is a generalization of the subs command, which only handles syntactic substitution. Therefore 'subs' is not the appropriate routine for your problem. For example the term x^3 can be changed with `subs', but the parameter E must be written without ' (Apostrophe). >subs(x^3 = z, E); y^2 = z+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2. A call of subs(...., 'E') try to substitute something in the name E since 'E' is unevaluated. One way to do your work is to use `simplify/siderels` : E:=y^2 = x^3+(1/4*a[1]^2+a[2])*x^2+(1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]]^4; eqs := a[1]^2+4*a[2] = b[2] > , 2*a[4]+a[1]*a[3] = b[4] > , a[3]^4+4*a[6] = b[6] > ; > simplify(E, {eqs}); 2 3 2 y = x + 1/4 x b[2] + 1/2 x b[4] + 1/4 b[6] (I have set the last term to 1/4*a[3]^4 instead of 1/4*a[3]^2 to make the substitution meaningful) E. Elbraechter ---------------------------------- E-Mail: Date: 22-Nov-2000 Time: 10:55:52 ---------------------------------- -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: Stanley J Houghton Date: Wed, 22 Nov 2000 13:24:12 +0000 To: zxl Subject: simplify or subs You need to use algsubs but it only takes one substitution equation at a time. Thus apply it sequentially in this way: > `E`:= > y^2 = x^3+(1/4*a[1]^2+a[2])*x^2+ > (1/2*a[1]*a[3]+a[4])*x+a[6]+1/4*a[3]^2; > algsubs(a[1]^2+4*a[2]=b[2],`E`); > algsubs(2*a[4]+a[1]*a[3]=b[4],%); > algsubs(a[3]^2+4*a[6]=b[6],%); I think this gives you what you want. Incidentally, note that I reduced the fourth power of a[3] in the last condition to the second power. From the equation `E`, I assume this is what you wanted. Regards Stan

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