$SPAD/src/input davis.input

Timothy Daly December 3, 2016

Abstract

From Davis, Phillip and Rabinowitz, Phillip “Method of Numerical Integration” Academic Press 1984

Contents

2

— * —

)set break resume
)spool davis.output
)set message test on
)set message auto off
)clear all
--S 1 of 101
f2:=1/(1+t^4)
--R
--R
--R           1
--R   (1)  ------
--R         4
--R        t  + 1
--R                                          Type: Fraction(Polynomial(Integer))
--E 1
--S 2 of 101
i2:=integrate(f2,t)
--R
--R
--R   (2)
--R        +-+      +-+    2         +-+        +-+    2
--R       \|2 log(t\|2  + t  + 1) - \|2 log(- t\|2  + t  + 1)
--R     +
--R           +-+         1          +-+         1
--R       - 2\|2 atan(---------) - 2\|2 atan(---------)
--R                     +-+                    +-+
--R                   t\|2  - 1              t\|2  + 1
--R  /
--R     8
--R                                         Type: Union(Expression(Integer),...)
--E 2
--S 3 of 101
d2:=integrate(f2,x=0,t)
--R
--R   There are 8 exposed and 1 unexposed library operations named
--R      integrate having 3 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named

--R      integrate with argument type(s)
--R                        Fraction(Polynomial(Integer))
--R                        Equation(Polynomial(Integer))
--R                                 Variable(t)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 3
--S 4 of 101
a2:=1/(4*sqrt(2))*log((x^2+x*sqrt(2)+1)/(x^2-x*sqrt(2)+1))+_
    (1/2*sqrt(2))*(atan(x/(sqrt(2)-x))+atan(x/(sqrt(2)+x)))
--R
--R
--R                    +-+    2
--R         +-+    - x\|2  - x  - 1      +-+         x         +-+         x
--R        \|2 log(----------------) + 4\|2 atan(--------) + 4\|2 atan(--------)
--R                   +-+    2                    +-+                   +-+
--R                 x\|2  - x  - 1               \|2  - x              \|2  + x
--R   (3)  ---------------------------------------------------------------------
--R                                          8
--R                                                    Type: Expression(Integer)
--E 4
--S 5 of 101
r2:=""
--R
--R
--R   (4)  ""
--R                                                                 Type: String
--E 5
--S 6 of 101
f56:=sin(%pi*x)
--R
--R
--R   (5)  sin(%pi x)
--R                                                    Type: Expression(Integer)
--E 6
--S 7 of 101
i56:=integrate(f56,x)
--R
--R
--R          cos(%pi x)
--R   (6)  - ----------
--R              %pi
--R                                         Type: Union(Expression(Integer),...)
--E 7

--S 8 of 101
d56:=integrate(f65,x=0..1)
--R
--R
--R   (7)  f65
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 8
--S 9 of 101
a56:=2/%pi
--R
--R
--R         2
--R   (8)  ---
--R        %pi
--R                                                                     Type: Pi
--E 9
--S 10 of 101
r56:=""
--R
--R
--R   (9)  ""
--R                                                                 Type: String
--E 10
--S 11 of 101
f57:=f(x)
--R
--R   There are no library operations named f
--R      Use HyperDoc Browse or issue
--R                                 )what op f
--R      to learn if there is any operation containing " f " in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named f
--R      with argument type(s)
--R                                 Variable(x)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 11
--S 12 of 101
i57:=integrate(f57,x)
--R
--R
--R   (10)  f57 x
--R                                          Type: Polynomial(Fraction(Integer))
--E 12

--S 13 of 101
d57:=integrate(f57,a..b)
--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--R                                Variable(f57)
--R                               Segment(Symbol)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 13
--S 14 of 101
a57:=((b-a)/6)*(f(a)+4*f((a+b)/2)+f(b))
--R
--R   There are no library operations named f
--R      Use HyperDoc Browse or issue
--R                                 )what op f
--R      to learn if there is any operation containing " f " in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named f
--R      with argument type(s)
--R                                 Variable(a)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 14
--S 15 of 101
r57:="degree(f) <= 3"
--R
--R
--R   (11)  "degree(f) <= 3"
--R                                                                 Type: String
--E 15
--S 16 of 101
f148:=exp(x^2)*cos(n*x)
--R

--R
--R                    2
--R                   x
--R   (12)  cos(n x)%e
--R                                                    Type: Expression(Integer)
--E 16
--S 17 of 101
i148:=integrate(f148,x)
--R
--R
--R            x              2
--R          ++             %K
--R   (13)   |   cos(%K n)%e   d%K
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 17
--S 18 of 101
d148:=integrate(f148,x=0..%pi)
--R
--R
--R   (14)  "failed"
--R                                                Type: Union(fail: failed,...)
--E 18
--S 19 of 101
a148:=((-1)^n/n^2)*2*%pi*exp(%pi^2)
--R
--R
--R                   2
--R                %pi      n
--R         2%pi %e    (- 1)
--R   (15)  -----------------
--R                  2
--R                 n
--R                                                    Type: Expression(Integer)
--E 19
--S 20 of 101
r148:=""
--R
--R
--R   (16)  ""
--R                                                                 Type: String
--E 20
--S 21 of 101
f153:=x*cos(x)*sin(n*x)
--R

--R
--R   (17)  x cos(x)sin(n x)
--R                                                    Type: Expression(Integer)
--E 21
--S 22 of 101
i153:=integrate(f153,x)
--R
--R
--R   (18)
--R            2                  2
--R       ((- n  + 1)x sin(x) + (n  + 1)cos(x))sin(n x) - 2n cos(n x)sin(x)
--R     +
--R           3
--R       (- n  + n)x cos(x)cos(n x)
--R  /
--R      4     2
--R     n  - 2n  + 1
--R                                         Type: Union(Expression(Integer),...)
--E 22
--S 23 of 101
d153:=integrate(f153,x=0..2*%pi)
--R
--R
--R           2                        3
--R         (n  + 1)sin(2n %pi) + (- 2n  + 2n)%pi cos(2n %pi)
--R   (19)  -------------------------------------------------
--R                             4     2
--R                            n  - 2n  + 1
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 23
--S 24 of 101
a153a:=-%pi/2
--R
--R
--R           %pi
--R   (20)  - ---
--R            2
--R                                                                     Type: Pi
--E 24
--S 25 of 101
r153a:="n=1"
--R
--R
--R   (21)  "n=1"
--R                                                                 Type: String
--E 25

--S 26 of 101
a153b:=-2*n*%pi/(n^2-1)
--R
--R
--R           2n %pi
--R   (22)  - ------
--R            2
--R           n  - 1
--R                                                    Type: Expression(Integer)
--E 26
--S 27 of 101
r153b:="n != 1"
--R
--R
--R   (23)  "n != 1"
--R                                                                 Type: String
--E 27
--S 28 of 101
fa154:=x*cos(50*x)*sin(n*x)
--R
--R
--R   (24)  x cos(50x)sin(n x)
--R                                                    Type: Expression(Integer)
--E 28
--S 29 of 101
ia154:=integrate(fa154,x)
--R
--R
--R   (25)
--R              2                         2
--R       ((- 50n  + 125000)x sin(50x) + (n  + 2500)cos(50x))sin(n x)
--R     +
--R                                     3
--R       - 100n cos(n x)sin(50x) + (- n  + 2500n)x cos(50x)cos(n x)
--R  /
--R      4        2
--R     n  - 5000n  + 6250000
--R                                         Type: Union(Expression(Integer),...)
--E 29
--S 30 of 101
da154:=integrate(fa154,x=0..2*%pi)
--R
--R
--R           2                           3
--R         (n  + 2500)sin(2n %pi) + (- 2n  + 5000n)%pi cos(2n %pi)

--R   (26)  -------------------------------------------------------
--R                           4        2
--R                          n  - 5000n  + 6250000
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 30
--S 31 of 101
aa154:=2*n*%pi/(2500-n^2)
--R
--R
--R             2n %pi
--R   (27)  - ---------
--R            2
--R           n  - 2500
--R                                                    Type: Expression(Integer)
--E 31
--S 32 of 101
ra154:="n != 50"
--R
--R
--R   (28)  "n != 50"
--R                                                                 Type: String
--E 32
--S 33 of 101
fb154:=x*sin(n*x)/sqrt(1-(x^2)/(4*%pi^2))
--R
--R
--R            x sin(n x)
--R   (29)  ---------------
--R          +------------+
--R          |   2       2
--R          |- x  + 4%pi
--R          |------------
--R          |        2
--R         \|    4%pi
--R                                                    Type: Expression(Integer)
--E 33
--S 34 of 101
ib154:=integrate(fb154,x)
--R
--R
--R            x
--R          ++   %K sin(%K n)
--R   (30)   |   -------------- d%K
--R         ++    +-----------+
--R               |    2     2
--R               |4%pi  - %K

--R               |-----------
--R               |       2
--R              \|   4%pi
--R                                         Type: Union(Expression(Integer),...)
--E 34
--S 35 of 101
db154:=integrate(fb154,x=0..2*%pi)
--R
--R
--R   (31)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 35
--S 36 of 101
ab154:=2*%pi^3*J(1,2*%pi*n) -- J(n,m) is the Bessel function
--R
--R  Line 406: --R
--R  Line 407: --R
--R  Line 408: --R   (31)  potentialPole
--R  Line 409: --R                                         Type: Union(pole: potentialPole,...)
--R  Line 410: --E 35
--R  Line 411:
--R  Line 412: --S 36 of 101
--R  Line 413: ab154:=2*%pi^3*J(1,2*%pi*n) -- J(n,m) is the Bessel function
--R  Error   : Quote added at end of line.
--R   1 error(s) parsing
--R   There are no library operations named J
--R      Use HyperDoc Browse or issue
--R                                 )what op J
--R      to learn if there is any operation containing " J " in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named J
--R      with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 36
--S 37 of 101
rb154:="singularity at x=2*%pi
--R
--R
--R   (32)  "singularity at x=2*%pi"
--R                                                                 Type: String
--E 37

--S 38 of 101
f155:=log(x)*sin(n*x)
--R
--R
--R   (33)  log(x)sin(n x)
--R                                                    Type: Expression(Integer)
--E 38
--S 39 of 101
i155:=integrate(f155,x)
--R
--R
--R            x
--R          ++
--R   (34)   |   log(%K)sin(%K n)d%K
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 39
--S 40 of 101
d155:=integrate(f155,x=0..2*%pi)
--R
--R
--R   (35)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 40
--S 41 of 101
a155:=(-1/n)*(y+log(2*n*%pi)-Ci(2*n*%pi)) -- y ~ .577215665 Ci is cosine int.
--R
--R
--R         - log(2n %pi) + Ci(2n %pi) - y
--R   (36)  ------------------------------
--R                        n
--R                                                    Type: Expression(Integer)
--E 41
--S 42 of 101
r155:="singularity at x=0"
--R
--R
--R   (37)  "singularity at x=0"
--R                                                                 Type: String
--E 42
--S 43 of 101
f210:=exp(-x^2)
--R
--R
--R              2

--R           - x
--R   (38)  %e
--R                                                    Type: Expression(Integer)
--E 43
--S 44 of 101
i210:=integrate(f210,x)
--R
--R
--R                +---+
--R         erf(x)\|%pi
--R   (39)  ------------
--R               2
--R                                         Type: Union(Expression(Integer),...)
--E 44
--S 45 of 101
d210:=integrate(f210,x=0..%plusInfinity)
--R
--R
--R          +---+
--R         \|%pi
--R   (40)  ------
--R            2
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 45
--S 46 of 101
a210:=sqrt(%pi)/2
--R
--R
--R          +---+
--R         \|%pi
--R   (41)  ------
--R            2
--R                                                    Type: Expression(Integer)
--E 46
--S 47 of 101
r210:=""
--R
--R
--R   (42)  ""
--R                                                                 Type: String
--E 47
--S 48 of 101
f212:=sech(x)^2
--R
--R

--R                2
--R   (43)  sech(x)
--R                                                    Type: Expression(Integer)
--E 48
--S 49 of 101
i212:=integrate(f212,x)
--R
--R
--R                               2
--R   (44)  - -----------------------------------------
--R                  2                            2
--R           sinh(x)  + 2cosh(x)sinh(x) + cosh(x)  + 1
--R                                         Type: Union(Expression(Integer),...)
--E 49
--S 50 of 101
d212:=integrate(f212,x=%minusInfinity..%plusInfinity)
--R
--R
--R   (45)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 50
--S 51 of 101
a212:=2
--R
--R
--R   (46)  2
--R                                                        Type: PositiveInteger
--E 51
--S 52 of 101
r212:=""
--R
--R
--R   (47)  ""
--R                                                                 Type: String
--E 52
--S 53 of 101
fa238:=exp(-x)*sin(w*x)
--R
--R
--R           - x
--R   (48)  %e   sin(w x)
--R                                                    Type: Expression(Integer)
--E 53
--S 54 of 101

ia238:=integrate(fa238,x)
--R
--R
--R             - x                       - x
--R         - %e   sin(w x) - w cos(w x)%e
--R   (49)  ---------------------------------
--R                        2
--R                       w  + 1
--R                                         Type: Union(Expression(Integer),...)
--E 54
--S 55 of 101
da238:=integrate(fa238,x=0..%plusInfinity)
--R
--R
--R            w
--R   (50)  ------
--R          2
--R         w  + 1
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 55
--S 56 of 101
aa238:=w/(1+w^2)
--R
--R
--R            w
--R   (51)  ------
--R          2
--R         w  + 1
--R                                          Type: Fraction(Polynomial(Integer))
--E 56
--S 57 of 101
ra238:=""
--R
--R
--R   (52)  ""
--R                                                                 Type: String
--E 57
--S 58 of 101
fb238:=(x/(1+x^2))*sin(w*x)
--R
--R
--R         x sin(w x)
--R   (53)  ----------
--R            2
--R           x  + 1
--R                                                    Type: Expression(Integer)

--E 58
--S 59 of 101
ib238:=integrate(fb238,x)
--R
--R
--R            x
--R          ++  %K sin(%K w)
--R   (54)   |   ------------ d%K
--R         ++        2
--R                 %K  + 1
--R                                         Type: Union(Expression(Integer),...)
--E 59
--S 60 of 101
db238:=integrate(fb238,x=0..%plusInfinity)
--R
--R
--R   (55)  "failed"
--R                                                Type: Union(fail: failed,...)
--E 60
--S 61 of 101
ab238:=%pi*exp(-w)/2
--R
--R
--R               - w
--R         %pi %e
--R   (56)  ---------
--R             2
--R                                                    Type: Expression(Integer)
--E 61
--S 62 of 101
rb238:=""
--R
--R
--R   (57)  ""
--R                                                                 Type: String
--E 62
--S 63 of 101
f239:=sin(x/2)^2*sin(w*x)/x
--R
--R
--R             x 2
--R         sin(-) sin(w x)
--R             2
--R   (58)  ---------------
--R                x

--R                                                    Type: Expression(Integer)
--E 63
--S 64 of 101
i239:=integrate(f239,x)
--R
--R
--R                  %K 2
--R            x sin(--) sin(%K w)
--R          ++       2
--R   (59)   |   ----------------- d%K
--R         ++           %K
--R                                         Type: Union(Expression(Integer),...)
--E 64
--S 65 of 101
d239:=integrate(f239,x=0..%plusInfinity)
--R
--R
--R   (60)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 65
--S 66 of 101
a239a:=%pi/4
--R
--R
--R         %pi
--R   (61)  ---
--R          4
--R                                                                     Type: Pi
--E 66
--S 67 of 101
r239a:="w<1"
--R
--R
--R   (62)  "w<1"
--R                                                                 Type: String
--E 67
--S 68 of 101
a239b:=%pi/8
--R
--R
--R         %pi
--R   (63)  ---
--R          8
--R                                                                     Type: Pi
--E 68

--S 69 of 101
r239b:="w=1"
--R
--R
--R   (64)  "w=1"
--R                                                                 Type: String
--E 69
--S 70 of 101
a239c:=0
--R
--R
--R   (65)  0
--R                                                     Type: NonNegativeInteger
--E 70
--S 71 of 101
r239c:="w>1"
--R
--R
--R   (66)  "w>1"
--R                                                                 Type: String
--E 71
--S 72 of 101
f385:=x
--R
--R
--R   (67)  x
--R                                                            Type: Variable(x)
--E 72
--S 73 of 101
i385:=integrate(f385,x)
--R
--R
--R         1  2
--R   (68)  - x
--R         2
--R                                          Type: Polynomial(Fraction(Integer))
--E 73
--S 74 of 101
d385:=integrate(f385,x=0..1)
--R
--R
--R         1
--R   (69)  -
--R         2

--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 74
--S 75 of 101
a385:=1/2
--R
--R
--R         1
--R   (70)  -
--R         2
--R                                                      Type: Fraction(Integer)
--E 75
--S 76 of 101
r385:=""
--R
--R
--R   (71)  ""
--R                                                                 Type: String
--E 76
--S 77 of 101
f388:=x^2
--R
--R
--R          2
--R   (72)  x
--R                                                    Type: Polynomial(Integer)
--E 77
--S 78 of 101
i388:=integrate(f388,x)
--R
--R
--R         1  3
--R   (73)  - x
--R         3
--R                                          Type: Polynomial(Fraction(Integer))
--E 78
--S 79 of 101
d388:=integrate(f388,x=0..1)
--R
--R
--R         1
--R   (74)  -
--R         3
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 79

--S 80 of 101
a388:=1/3
--R
--R
--R         1
--R   (75)  -
--R         3
--R                                                      Type: Fraction(Integer)
--E 80
--S 81 of 101
a388:=""
--R
--R
--R   (76)  ""
--R                                                                 Type: String
--E 81
--S 82 of 101
fa453:=abs(x^2+y^2-0.25)
--R
--R
--R              2    2
--R   (77)  abs(y  + x  - 0.25)
--R                                                      Type: Expression(Float)
--E 82
--S 83 of 101
ia453:=integrate(integrate(fa453,x),y)
--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--R                              Expression(Float)
--R                                 Variable(x)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 83
--S 84 of 101
da453:=integrate(integrate(fa453,x=-1..1),y=-1..1)

--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--R                              Expression(Float)
--R                           SegmentBinding(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 84
--S 85 of 101
aa453:=(5/3)+(%pi/16)
--R
--R
--R         3%pi + 80
--R   (78)  ---------
--R             48
--R                                                                     Type: Pi
--E 85
--S 86 of 101
ra453:="singularity along circle with radius = 1/2"
--R
--R
--R   (79)  "singularity along circle with radius = 1/2"
--R                                                                 Type: String
--E 86
--S 87 of 101
fb453:=1/(1-x*y)
--R
--R
--R              1
--R   (80)  - -------
--R           x y - 1
--R                                          Type: Fraction(Polynomial(Integer))
--E 87
--S 88 of 101
ib453:=integrate(integrate(fb453,x),y)
--R

--R
--R            y
--R          ++    log(%K x - 1)
--R   (81)   |   - ------------- d%K
--R         ++           %K
--R                                         Type: Union(Expression(Integer),...)
--E 88
--S 89 of 101
db453:=integrate(integrate(fb453,x=0..1),y=0..1)
--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--IUnion(f1: OrderedCompletion(Expression(Integer)),f2: ...
--R                     SegmentBinding(NonNegativeInteger)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 89
--S 90 of 101
ab453:=%pi^2/6
--R
--R
--R            2
--R         %pi
--R   (82)  ----
--R           6
--R                                                                     Type: Pi
--E 90
--S 91 of 101
rb453:=""
--R
--R
--R   (83)  ""
--R                                                                 Type: String
--E 91
--S 92 of 101
fc453:=sqrt(abs(x-y))

--R
--R
--R          +----------+
--R   (84)  \|abs(y - x)
--R                                                    Type: Expression(Integer)
--E 92
--S 93 of 101
ic453:=integrate(integrate(fc453,x),y)
--R
--R
--RDaly Bug
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 93
--S 94 of 101
dc453:=integrate(integrate(fc453,x=0..1),y=0..1)
--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--IUnion(f1: OrderedCompletion(Expression(Integer)),f2: ...
--R                     SegmentBinding(NonNegativeInteger)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 94
--S 95 of 101
ac453:=8/15
--R
--R
--R          8
--R   (85)  --
--R         15
--R                                                      Type: Fraction(Integer)
--E 95

--S 96 of 101
rc453:="singularity along x=y"
--R
--R
--R   (86)  "singularity along x=y"
--R                                                                 Type: String
--E 96
--S 97 of 101
f455:=abs(x^2+y^2+z^2-.125)
--R
--R
--R              2    2    2
--R   (87)  abs(z  + y  + x  - 0.125)
--R                                                      Type: Expression(Float)
--E 97
--S 98 of 101
i455:=integrate(integrate(integrate(f455,x),y),z)
--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--R                              Expression(Float)
--R                                 Variable(x)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 98
--S 99 of 101
d455:=integrate(integrate(integrate(f455,x=-1..1),y=-1..1),z=-1..1)
--R
--R   There are 15 exposed and 7 unexposed library operations named
--R      integrate having 2 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op integrate
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug

--R   Cannot find a definition or applicable library operation named
--R      integrate with argument type(s)
--R                              Expression(Float)
--R                           SegmentBinding(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 99
--S 100 of 101
a455:=7+%pi/120
--R
--R
--R         %pi + 840
--R   (88)  ---------
--R            120
--R                                                                     Type: Pi
--E 100
--S 101 of 101
r455:="singularity along sphere of radius 1/2"
--R
--R
--R   (89)  "singularity along sphere of radius 1/2"
--R                                                                 Type: String
--E 101
)spool
)lisp (bye)

———-

References^{[1] nothing}

26