{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "Help Head ing" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "Tim es" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "Maple O utput" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 8 "Advice: " }{TEXT -1 27 "As sume doesn't affect solve" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 238 "The assume command is used with symbolic variable s that are not assigned values, and tells Maple that it can apply rule s that would be appropriate when the variable has certain properties ( e.g. is an integer). This primarily affects the " }{MPLTEXT 0 21 8 "s implify" }{TEXT -1 19 " command. Thus if " }{MPLTEXT 0 21 1 "x" } {TEXT -1 28 " is assumed to be positive, " }{XPPEDIT 18 0 "sqrt(x^2)" "6#-%%sqrtG6#*$%\"xG\"\"#" }{TEXT -1 22 " can be simplified to " } {XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 58 "However, these assumptions do n ot restrict the values for " }{MPLTEXT 0 21 1 "x" }{TEXT -1 25 " that \+ can be returned by " }{MPLTEXT 0 21 5 "solve" }{TEXT -1 74 " and its r elated commands. There are other ways to restrict these values." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 10 " Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "assume(x, posi tive);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify(sqrt(x^2 ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#x|irG" }}}{PARA 0 "" 0 "" {TEXT -1 17 "In this example, " }{MPLTEXT 0 21 5 "solve" }{TEXT -1 58 " finds both real and complex solutions; the assumption on " } {MPLTEXT 0 21 1 "x" }{TEXT -1 15 " has no effect." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(x^4 + 2*x = 20, x);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6&\"\"#,(*$),&\"$2\"\"\"\"*&\"\"$F)-%%sqrtG6#\"%H8F)F)# F)F+F)#!\"\"F+*&#\"\")F+F)*$)F'#F)F+F)F2F)#F#F+F2,*F%#F)\"\"'*&#\"\"%F +F)*&F)F)*$)F'#F)F+F)F2F)F2#F#F+F2*(^##F)F#F)-F-6#F+F),&F%F1*&#F5F+F)F @F)F2F)F),*F%F;*&#F?F+F)F@F)F2#F#F+F2*(^##F2F#F)FHF)FJF)F)" }}}{PARA 0 "" 0 "" {TEXT -1 39 "Finding positive solutions in \"solve\": " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "solve(\{y^4 + 2*y = 20, y > \+ 0\}, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#/%\"yG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 23 "Finding real solutions:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "solve(\{y^4 + 2*y = 20, y > -infinity\}, y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$<#/%\"yG\"\"#<#/F%-%'RootOfG6$,**$)%#_ ZG\"\"$\"\"\"F1*&F&F1)F/F&F1F1*&\"\"%F1F/F1F1\"#5F1$!+/LgBA!\"*" }}} {PARA 0 "" 0 "" {TEXT -1 26 "Finding integer solutions:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "isolve(y^4 + 2*y = 20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#/%\"yG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 32 "Real (numerical) solutions with " }{MPLTEXT 0 21 6 "fsolve" } {TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(y^4 \+ + 2*y = 20, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$!+/LgBA!\"*$\"\"# \"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 27 "Restricting to an interval:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "fsolve(y^4 + 2*y = 20, y = 0 .. infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"#\"\"!" }}} {PARA 0 "" 0 "" {TEXT -1 19 "Another option for " }{MPLTEXT 0 21 6 "fs olve" }{TEXT -1 4 " is " }{MPLTEXT 0 21 31 "avoid = \{variable = value , ...\}" }{TEXT -1 14 " which causes " }{MPLTEXT 0 21 6 "fsolve" } {TEXT -1 103 " to omit one or several known solutions. This is especi ally useful for non-polynomial equations where " }{MPLTEXT 0 21 6 "fso lve" }{TEXT -1 27 " only returns one solution." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(y^3 + 2 = 20/y, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++?!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "fsolve(y^3 + 2 = 20/y, y, avoid = \{y=2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+/LgBA!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 58 "However, \+ it doesn't seem to work for systems of equations:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "fsolve(\{x+2*y=2,x^2-y^2=0\},\{x,y\}, avoid= \{x=-2.000000000,y=2.000000000\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# <$/%#x|irG$!+++++?!\"*/%\"yG$\"+++++?F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fsolve(\{x+2*y=2,x^2-y^2=0\},\{x,y\}, x=0..infinity); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#x|irG$\"+nmmmm!#5/%\"yGF&" }} }}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See also:" }{TEXT -1 1 " " } {HYPERLNK 17 "assume" 2 "assume" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "De claring the type of an argument" 2 "Declaring_the_type_of_an_argument " "" }{TEXT -1 2 ", " }{HYPERLNK 17 "fsolve" 2 "fsolve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "isolve" 2 "isolve" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "solve" 2 "solve" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 22 "Maple Advisor Database" }{TEXT 256 18 " R. Israel, 1997" }}}} {MARK "2 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }