Re: new user help

*To*: mathgroup at smc.vnet.net*Subject*: [mg13406] Re: new user help*From*: phbrf at t-online.de (Peter Breitfeld)*Date*: Thu, 23 Jul 1998 03:32:50 -0400*Organization*: das ist ein weites Feld ...*References*: <6okkvj$1md@smc.vnet.net> <6ous3s$jh3@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Allan Hayes <hay at haystack.demon.cc.uk> schrieb/wrote: : : John M. Dlugosz wrote in message <6okkvj$1md at smc.vnet.net>... : >I'm lost. I just don't know how to get started... : > : >The excersize I've chosen for myself is to start with : > : > x^2+y^2+4x-6y+4==0 : > : >and manipulate it into the form (x-h)^2+(y-k)^2==r^2 : > : >So... how do I "manipulate" the equasion? The functions like Expand, : >Factor, etc. don't help much. I my calculator (an HP48) I can point to : >specific subexpressions and apply operations to them, like factor, : >distribute, changing forms, etc. : > : >How do I collect the x's together in parens, the y's in parens, and : >complete the squares? Doing it on paper defeats the point! I want to : >learn how to "do math" using this tool. That's more than just asking : >"OK, what's X?". It means manipulating things and arranging them, : >getting to know how the symbols all fit together. : > : >--John : Try to use a replacement-rule: eq = x^2+y^2+4x-6y+4==0 quadRule = { x_^2 + x_ -> (x+1/2)^2-1/4, [1] x_^2 + b_ x_ -> (x+b/2)^2-b^2/4, a_ x^2 + x_ -> a(x-1/(2a))^2-1/(4a), a_ x_^2 + b_ x_ ->a(x+b/(2a))^2-b^2/(4a) } Then do In: qf=eq //. quadRule [2] Out: -9 + (2+x)^2 +(-3+y)^2==0 In: (#-qf[[1,1]])& /@ qf [3] Out: (2+x)^2 + (-3+y)^2 == 9 [1] To make this work in the general case, you have to give all the four rules, because the FullForm of x^2+4x doesn't match a_ x_^2 + b_ x_ because there is no "a" etc. [2] If you don't use ReplaceRepeated here, you only get the x-term in quadratic form [3] Mathematica orders term always with numbers in the first place, so qf[[1,1] represents the "-9" in this example. (#-qf[[1]])& is a pure function, which subtracts qf[[1]] from the given expression. Here I map this function on the equation (via /@) so the "-9" will be sub- tracted from both sides of the equation qf. I don't think there is a simple way to write the 9 as 3^2, because Mathematica will simplify 3^2 to 9 immediately. es gruesst Peter -- =--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--= P e t e r B r e i t f e l d eMail: phbrf at t-online.de Kreuzgasse 4, 88348 Saulgau, Germany PGP public key available =--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=--=