{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {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 {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 unevalua ted definite integral, sum, or product " }}{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 variable name (possibly indexed)" } }{PARA 0 "" 0 "" {MPLTEXT 0 21 6 "vflag " }{TEXT -1 27 "- (optional) t rue or false." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 12 "Description:" } }{PARA 15 "" 0 "" {TEXT -1 51 "Splits up an integral, sum or product a t the value " }{MPLTEXT 0 21 1 "a" }{TEXT -1 68 " of the dummy variabl e, separating the values of the dummy variable " }{MPLTEXT 0 21 3 "< a " }{TEXT -1 11 " and those " }{MPLTEXT 0 21 4 ">= a" }{TEXT -1 50 " in to separate integrals, sums or products. Thus " }{XPPEDIT 18 0 "Int(f (x), x = 0 .. 1)" "6#-%$IntG6$-%\"fG6#%\"xG/F);\"\"!\"\"\"" }{TEXT -1 9 " becomes " }{XPPEDIT 18 0 "Int(f(x), x = 0 .. a) + Int(f(x), x = a \+ .. 1)" "6#,&-%$IntG6$-%\"fG6#%\"xG/F*;\"\"!%\"aG\"\"\"-F%6$-F(6#F*/F*; F.\"\"\"F/" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "Sum(f[i], i = m .. n) " "6#-%$SumG6$&%\"fG6#%\"iG/F);%\"mG%\"nG" }{TEXT -1 9 " becomes " } {XPPEDIT 18 0 "Sum(f[i],i=m..a-1) + Sum(f[i],i=a..n)" "6#,&-%$SumG6$&% \"fG6#%\"iG/F*;%\"mG,&%\"aG\"\"\"\"\"\"!\"\"F0-F%6$&F(6#F*/F*;F/%\"nGF 0" }{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 instea d 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 ensur e that the integral, sum or product is not evaluated before being spli t." }}{PARA 15 "" 0 "" {TEXT -1 21 "If 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 nested integrals, sums or products, the outermost one is split." }}{PARA 15 "" 0 "" {TEXT -1 51 "No split ting is done if it is known that the value " }{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 even if " }{MPLTEXT 0 21 1 "a" }{TEXT -1 86 " is outside the interval, according to the conventions M aple uses: e.g. for a sum, if " }{XPPEDIT 18 0 "a < b-1" "6#2%\"aG,&% \"bG\"\"\"\"\"\"!\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "Sum(f[i], i = \+ b .. a) = - Sum(f[i], i = a+1 .. b-1)" "6#/-%$SumG6$&%\"fG6#%\"iG/F*;% \"bG%\"aG,$-F%6$&F(6#F*/F*;,&F.\"\"\"\"\"\"F7,&F-F7\"\"\"!\"\"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 cas e of a sum or product, if it is numeric it must be an integer." }} {PARA 15 "" 0 "" {TEXT -1 57 "For a sum or product, unless the optiona l 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 t he split the difference between the bounds is an integer, 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)" "6#-%$SumG6$&%\"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]" "6#,(-%$SumG6$&%\"bG6#%\"iG/F*; \"\"\",&%\"nG\"\"\"\"\"\"!\"\"F0&F(6#F/F0&F(6#,&F/F0\"\"\"F0F0" } {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)" "6#,&-%$SumG6$&%\"bG6#%\"iG/ F*;\"\"\",&%\"nG\"\"\"\"\"\"!\"\"F0-F%6$&F(6#F*/F*;F/,&F/F0\"\"\"F0F0 " }{TEXT -1 18 ". In the case of " }{MPLTEXT 0 21 3 "Int" }{TEXT -1 46 ", no evaluation is done. The non-inert forms " }{MPLTEXT 0 21 3 " sum" }{TEXT -1 2 ", " }{MPLTEXT 0 21 7 "product" }{TEXT -1 5 " and " } {MPLTEXT 0 21 3 "int" }{TEXT -1 34 " will always attempt to evaluate. \+ " }}{PARA 15 "" 0 "" {MPLTEXT 0 21 7 "splitup" }{TEXT -1 73 " is autom atically mapped into arrays, lists, sets, functions, +, * and ^." }} {PARA 15 "" 0 "" {TEXT -1 106 "This function is part of the Maple Advi sor Database library, and must be loaded before use by the command " } {MPLTEXT 0 21 17 "readlib(splitup);" }{TEXT -1 1 "." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "readlib(splitup):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "splitup(Int(f(x),x=a..c), b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, &-%$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 .. inf inity) - 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 "Product " 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, 1 997" }}}}{MARK "3 0 0" 4 }{VIEWOPTS 1 1 0 1 1 1803 }