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{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 26 17 "Calling Sequence:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "sp
litup(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)" "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$-F(6#F*/F*;F.F/F/" }{TEXT -1 5 " and " }
{XPPEDIT 18 0 "Sum(f[i], i = m .. n)" "6#-%$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$&%\"fG6#%\"iG/F*;%\"mG,&%\"aG\"\"\"F0!
\"\"F0-F%6$&F(6#F*/F*;F/%\"nGF0" }{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" "6#2%\"aG,&%\"bG\"\"\"F'!\"\"" }{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.\"\"\"
F7F7,&F-F7F7!\"\"F9" }{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 must be an in
teger." }}{PARA 15 "" 0 "" {TEXT -1 57 "For a sum or product, unless t
he 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 integer, that par
t 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);\"\"\",&%\"nGF,F,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*;\"\"\",&%\"
nGF-F-!\"\"F-&F(6#F/F-&F(6#,&F/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)" "6#,&-%$SumG6$&%\"bG6#%\"iG/F*;\"\"\",&%\"nGF-F-!\"\"
F--F%6$&F(6#F*/F*;F/,&F/F-F-F-F-" }{TEXT -1 18 ".  In the case of " }
{MPLTEXT 0 21 3 "Int" }{TEXT -1 46 ", no evaluation is done.  The non-
inert forms " }{MPLTEXT 0 21 3 "sum" }{TEXT -1 2 ", " }{MPLTEXT 0 21 
7 "product" }{TEXT -1 5 " and " }{MPLTEXT 0 21 3 "int" }{TEXT -1 34 " \+
will always attempt to evaluate. " }}{PARA 15 "" 0 "" {MPLTEXT 0 21 7 
"splitup" }{TEXT -1 73 " is automatically mapped into arrays, lists, s
ets, functions, +, * and ^." }}{PARA 15 "" 0 "" {TEXT -1 60 "This func
tion is part of the Maple Advisor Database library." }}}{SECT 0 {PARA 
3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "splitup(Int(f(x),x=a..c), b);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&-%$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 .. i
nfinity) - 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\"\"\"F4!\"\"F4-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 "0 0 1" 47 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }