{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "Help Heading" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "Function:" }{TEXT -1 47 " splitup - break up an integral, sum or product" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 26 17 "Calling Sequence:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "splitup(f, \+ a);" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 21 "splitup(f, a, vflag);" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 18 "splitup(f, x = a);" }}{PARA 0 "" 0 " " {MPLTEXT 0 21 25 "splitup(f, x = a, vflag);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 26 11 "Parameters:" }}{PARA 0 " " 0 "" {MPLTEXT 0 21 6 "f " }{TEXT -1 96 "- an expression, usually containing at least one unevaluated definite integral, sum, or produc t " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 6 "a " }{TEXT -1 68 "- a value for the dummy or index variable of the int, sum or product" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 6 "x " }{TEXT -1 51 "- a dummy or index va riable name (possibly indexed)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 6 "vfl ag " }{TEXT -1 27 "- (optional) true or false." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 12 "Description:" }}{PARA 15 "" 0 "" {TEXT -1 51 "Splits up an integral, sum or product at the value " }{MPLTEXT 0 21 1 "a" } {TEXT -1 68 " of the dummy variable, separating the values of the dumm y variable " }{MPLTEXT 0 21 3 "< a" }{TEXT -1 11 " and those " } {MPLTEXT 0 21 4 ">= a" }{TEXT -1 50 " into separate integrals, sums or products. Thus " }{XPPEDIT 18 0 "Int(f(x), x = 0 .. 1)" "-%$IntG6$-% \"fG6#%\"xG/F(;\"\"!\"\"\"" }{TEXT -1 9 " becomes " }{XPPEDIT 18 0 "In t(f(x), x = 0 .. a) + Int(f(x), x = a .. 1)" ",&-%$IntG6$-%\"fG6#%\"xG /F);\"\"!%\"aG\"\"\"-F$6$-F'6#F)/F);F-\"\"\"F." }{TEXT -1 5 " and " } {XPPEDIT 18 0 "Sum(f[i], i = m .. n)" "-%$SumG6$&%\"fG6#%\"iG/F(;%\"mG %\"nG" }{TEXT -1 9 " becomes " }{XPPEDIT 18 0 "Sum(f[i],i=m..a-1) + Su m(f[i],i=a..n)" ",&-%$SumG6$&%\"fG6#%\"iG/F);%\"mG,&%\"aG\"\"\"\"\"\"! \"\"F/-F$6$&F'6#F)/F);F.%\"nGF/" }{TEXT -1 1 "." }}{PARA 15 "" 0 "" {TEXT -1 16 "The inert forms " }{MPLTEXT 0 21 3 "Int" }{TEXT -1 2 ", \+ " }{MPLTEXT 0 21 3 "Sum" }{TEXT -1 2 ", " }{MPLTEXT 0 21 7 "Product" } {TEXT -1 24 " may be used instead of " }{MPLTEXT 0 21 3 "int" }{TEXT -1 2 ", " }{MPLTEXT 0 21 3 "sum" }{TEXT -1 5 ", or " }{MPLTEXT 0 21 7 "product" }{TEXT -1 81 " to ensure that the integral, sum or product i s not evaluated before being split." }}{PARA 15 "" 0 "" {TEXT -1 21 "I f the variable name " }{MPLTEXT 0 21 1 "x" }{TEXT -1 80 " is specified , only those integrals, sums or products with dummy variable named " } {MPLTEXT 0 21 1 "x" }{TEXT -1 94 " will be split. Otherwise, for neste d integrals, sums or products, the outermost one is split." }}{PARA 15 "" 0 "" {TEXT -1 51 "No splitting is done if it is known that the v alue " }{MPLTEXT 0 21 1 "a" }{TEXT -1 103 " is outside the interval of the integral, sum or product. Note that the result is still valid ev en if " }{MPLTEXT 0 21 1 "a" }{TEXT -1 86 " is outside the interval, a ccording to the conventions Maple uses: e.g. for a sum, if " } {XPPEDIT 18 0 "a < b-1" "2%\"aG,&%\"bG\"\"\"\"\"\"!\"\"" }{TEXT -1 2 " , " }{XPPEDIT 18 0 "Sum(f[i], i = b .. a) = - Sum(f[i], i = a+1 .. b-1 )" "/-%$SumG6$&%\"fG6#%\"iG/F);%\"bG%\"aG,$-F$6$&F'6#F)/F);,&F-\"\"\" \"\"\"F6,&F,F6\"\"\"!\"\"F:" }{TEXT -1 3 ". " }}{PARA 15 "" 0 "" {TEXT -1 10 "The value " }{MPLTEXT 0 21 1 "a" }{TEXT -1 98 " need not \+ be numeric, but in the case of a sum or product, if it is numeric it m ust be an integer." }}{PARA 15 "" 0 "" {TEXT -1 57 "For a sum or produ ct, unless the optional third argument " }{MPLTEXT 0 21 5 "vflag" } {TEXT -1 4 " is " }{MPLTEXT 0 21 5 "false" }{TEXT -1 144 ", if in any \+ of the results of the split the difference between the bounds is an in teger, that part is evaluated explicitly (even though it is a " } {MPLTEXT 0 21 3 "Sum" }{TEXT -1 4 " or " }{MPLTEXT 0 21 7 "Product" } {TEXT -1 12 "). Thus if " }{XPPEDIT 18 0 "Sum(b[i], i = 1 .. n+1)" " -%$SumG6$&%\"bG6#%\"iG/F(;\"\"\",&%\"nG\"\"\"\"\"\"F." }{TEXT -1 13 " \+ is split at " }{MPLTEXT 0 21 1 "n" }{TEXT -1 21 " the result would be \+ " }{XPPEDIT 18 0 "Sum(b[i],i=1..n-1) + b[n] + b[n+1]" ",(-%$SumG6$&%\" bG6#%\"iG/F);\"\"\",&%\"nG\"\"\"\"\"\"!\"\"F/&F'6#F.F/&F'6#,&F.F/\"\" \"F/F/" }{TEXT -1 6 ". If " }{MPLTEXT 0 21 5 "vflag" }{TEXT -1 4 " is " }{MPLTEXT 0 21 5 "false" }{TEXT -1 15 " this would be " }{XPPEDIT 18 0 "Sum(b[i],i=1..n-1) + Sum(b[i],i=n..n+1)" ",&-%$SumG6$&%\"bG6#%\" iG/F);\"\"\",&%\"nG\"\"\"\"\"\"!\"\"F/-F$6$&F'6#F)/F);F.,&F.F/\"\"\"F/ F/" }{TEXT -1 18 ". In the case of " }{MPLTEXT 0 21 3 "Int" }{TEXT -1 46 ", no evaluation is done. The non-inert forms " }{MPLTEXT 0 21 3 "sum" }{TEXT -1 2 ", " }{MPLTEXT 0 21 7 "product" }{TEXT -1 5 " and \+ " }{MPLTEXT 0 21 3 "int" }{TEXT -1 34 " will always attempt to evaluat e. " }}{PARA 15 "" 0 "" {MPLTEXT 0 21 7 "splitup" }{TEXT -1 73 " is au tomatically mapped into arrays, lists, sets, functions, +, * and ^." } }{PARA 15 "" 0 "" {TEXT -1 106 "This function is part of the Maple Adv isor Database library, and must be loaded before use by the command " }{MPLTEXT 0 21 17 "readlib(splitup);" }{TEXT -1 1 "." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "readlib(splitup):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "splitup(Int(f(x),x=a..c), b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$IntG6$-%\"fG6#%\"xG/F*;%\"aG%\"bG\"\"\"-F%6$F'/F*; F.%\"cGF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "splitup(Sum(b[ i], i=1 .. infinity) - Sum(b[i], i = 3 .. infinity), i = 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&&%\"bG6#\"\"\"F'&F%6#\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "splitup(Sum(Product(c[i,j], i=k .. \+ n), j = 1 .. m), i = p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$* &-%(ProductG6$&%\"cG6$%\"iG%\"jG/F-;%\"kG,&%\"pG\"\"\"!\"\"F4F4-F(6$F* /F-;F3%\"nGF4/F.;F4%\"mG" }}}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See \+ also:" }{TEXT -1 1 " " }{HYPERLNK 17 "Int" 2 "Int" "" }{TEXT -1 2 ", \+ " }{HYPERLNK 17 "Sum" 2 "Sum" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "Produ ct" 2 "Product" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "combine" 2 "combine " "" }{TEXT -1 2 ", " }{HYPERLNK 17 "assume" 2 "assume" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "interface" 2 "interface" "" }}}{SECT 0 {PARA 0 " " 0 "" {TEXT 26 22 "Maple Advisor Database" }{TEXT -1 17 " R. Israel, 1997" }}}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }