TeX 1995 July/TeX CD-ROM July 1995 (Disc 1)(Walnut Creek)(1995).ISO/web/reduce/rweb/appl/source/integrator.red

Text File | 1991-12-17 | 26.8 KB | 992 lines

%5:%
%line 72 "integrator.web"

symbolic$
write"Integrator package for REDUCE 3.4, $Revision: 0.92 $"$terpri()$
%9:%
%line 213 "integrator.web"

%line 214 "integrator.web"
put( 'initialize_equations, 'psopfn, 'initialize_equations1)$

%:9%%13:%
%line 294 "integrator.web"


global '(current_equation_set!*)$
current_equation_set!*:= 'equ$

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%line 382 "integrator.web"



fluid '(!*coefficient_check)$
!*coefficient_check:=t$
flag( '(coefficient_check), 'switch)$

%:18%%30:%
%line 597 "integrator.web"

%line 598 "integrator.web"


fluid '(!*polynomial_check)$
!*polynomial_check:=nil$
flag( '(polynomial_check), 'switch)$

%:30%%50:%
%line 955 "integrator.web"

%line 956 "integrator.web"


fluid '(!*allow_differentiation)$
!*allow_differentiation:=nil$
flag( '(allow_differentiation), 'switch)$

%:50%%61:%
%line 1185 "integrator.web"

%line 1186 "integrator.web"

fluid '(listpri_depth!*)$
listpri_depth!*:=40$

%:61%
%line 75 "integrator.web"

algebraic$

%:5%%10:%
%line 217 "integrator.web"

%line 218 "integrator.web"
lisp procedure initialize_equations1 specification_list;
begin scalar operator_name,total_used,variable_list,
specification,even_used,odd_used,
constant_operator,bracketname,function_name,function_list;
if length specification_list<5 then
rederr("INITIALIZE_EQUATIONS: wrong number of parameters");
if not idp(operator_name:=car specification_list)then
rederr("INITIALIZE_EQUATIONS: equations operator must be identifier");
if not fixp(total_used:=
reval car(specification_list:=cdr specification_list))
or total_used<0 then
rederr("INITIALIZE_EQUATIONS: total number of equations must be positive");
put(operator_name, 'total_used,total_used);
variable_list:=reval car(
specification_list:=cdr specification_list);
if atom variable_list or car variable_list neq 'list then
rederr("INITIALIZE_EQUATIONS: variable list must be algebraic list");
put(operator_name, 'variable_list,cdr variable_list);
%11:%
%line 265 "integrator.web"

specification_list:=cdr specification_list;
specification:=car specification_list;

if atom specification or length specification neq 4 or car specification neq 'list
or not idp(constant_operator:=cadr specification)or
not fixp(even_used:=reval caddr specification)or
not fixp(odd_used:=reval cadddr specification)
or even_used<0 or odd_used<0 then

msgpri("INITIALIZE_EQUATIONS: invalid declaration of",
specification,nil,nil,t);
put(operator_name, 'constant_operator,constant_operator);
if get(constant_operator, 'rtype)= 'algebra_generator then
put(operator_name, 'bracketname,
bracketname:=get(constant_operator, 'bracketname));

if get(constant_operator, 'rtype)= 'algebra_generator then
define_used(bracketname,list( 'list,even_used,odd_used))
else
begin
put(constant_operator, 'even_used,even_used);
put(constant_operator, 'odd_used,odd_used);
end

%:11%
%line 236 "integrator.web"
;
%12:%
%line 276 "integrator.web"

%line 277 "integrator.web"
for each function_specification in cdr specification_list do
begin

if atom function_specification or length function_specification neq 4 or car function_specification neq 'list
or not idp(function_name:=cadr function_specification)or
not fixp(even_used:=reval caddr function_specification)or
not fixp(odd_used:=reval cadddr function_specification)
or even_used<0 or odd_used<0 then

msgpri("INITIALIZE_EQUATIONS: invalid declaration of",
function_specification,nil,nil,t);

if get(function_name, 'rtype)= 'algebra_generator then
define_used(bracketname,list( 'list,even_used,odd_used))
else
begin
put(function_name, 'even_used,even_used);
put(function_name, 'odd_used,odd_used);
end;
function_list:=function_name . function_list;
end;
put(operator_name, 'function_list,function_list)

%:12%
%line 237 "integrator.web"
;
end$

%:10%%14:%
%line 298 "integrator.web"

%line 299 "integrator.web"
lisp operator use_equations;
lisp procedure use_equations operator_name;
begin
if idp operator_name then
current_equation_set!*:=operator_name
else rederr("USE_EQUATIONS: argument must be identifier");
end$

%:14%%15:%
%line 315 "integrator.web"

%line 316 "integrator.web"
lisp operator integrate_equation;
lisp procedure integrate_equation n;
begin scalar listpri_depth!*,total_used,equation,denominator,
solvable_kernel,solvable_kernels,df_list,df_kernel,
function_list,present_functions_list,variable_list,absent_variables,
polynomial_variables,equations_list,linear_functions_list,constants_list,
bracketname,df_terms,df_functions,
linear_functions,functions_and_constants_list,commutator_functions,
present_variables,
inhomogeneous_term,nr_of_variables,integration_variables,
forbidden_functions,differentiations_list,polynomial_order;
listpri_depth!*:=200;
terpri!* t;
%16:%
%line 348 "integrator.web"

if null(total_used:=get(current_equation_set!*, 'total_used))or
n>total_used then

msgpri("INTEGRATE_EQUATIONS: properly initialize",
current_equation_set!*,nil,nil,t);
if null(equation:=cadr assoc(list(current_equation_set!*,n),
get(current_equation_set!*, 'kvalue)))then

msgpri("INTEGRATE_EQUATION:",list(current_equation_set!*,n),
"is non-existent",nil,t);
denominator:=denr(equation:=simp!* equation);
equation:=numr equation;
if null equation then
 <<write current_equation_set!*,"(",n,") = 0";terpri!* t;

setk(list(current_equation_set!*,n),0);goto solved>>

%:16%
%line 329 "integrator.web"
;
%19:%
%line 398 "integrator.web"

df_list:=split_form(equation, '(df));
if null car df_list and
(cdr df_list)and length(cdr df_list)=1
then
if(solvable_kernel:=find_solvable_kernel(
solvable_kernels:=list(car car cdr df_list),
cdr df_list,denominator))then
 <<df_kernel:=cadr solvable_kernel;
setk(df_kernel,homogeneous_integration_of(solvable_kernel));
depl!*:=
delete(assoc(df_kernel,depl!*),depl!*);


 <<write current_equation_set!*,"(",n,"): ","Homogeneous integration of ";maprin solvable_kernel;terpri!* nil;

setk(list(current_equation_set!*,n),0);goto solved>> >>
else
 <<write"*** ",current_equation_set!*,"(",n,"): ","Homogeneous integration"," failed:";terpri!* t;
write"    coefficient not a number for ";
maprin
car solvable_kernels;terpri!* nil;
write"    Solvable with 'off coefficient_check'";
terpri!* t;goto solved>>

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%line 330 "integrator.web"
;
%27:%
%line 568 "integrator.web"

%28:%
%line 576 "integrator.web"

%line 577 "integrator.web"
function_list:=get(current_equation_set!*, 'function_list);
present_functions_list:=get_recursive_kernels(equation,function_list);
variable_list:=get(current_equation_set!*, 'variable_list);
absent_variables:=variable_list;
for each function in present_functions_list do
for each variable in
((if depl_entry then cdr depl_entry)where depl_entry=assoc(function,depl!*))do
absent_variables:=delete(variable,absent_variables)

%:28%
%line 569 "integrator.web"
;
%29:%
%line 591 "integrator.web"

%line 592 "integrator.web"
polynomial_variables:=absent_variables;
if !*polynomial_check then
polynomial_variables:=for each variable in polynomial_variables join
if polynomialp(equation,variable)then list(variable)

%:29%
%line 570 "integrator.web"
;
%32:%
%line 614 "integrator.web"

%line 615 "integrator.web"
equations_list:=multi_split_form(equation,polynomial_variables);
if length equations_list>1 then
 <<for each pc_pair in cdr
equations_list do
setk(list(current_equation_set!*,(total_used:=total_used+1)),
mk!*sq((cdr pc_pair) ./ 1));
if car equations_list then
setk(list(current_equation_set!*,(total_used:=total_used+1)),
mk!*sq((car equations_list) ./ 1));
write current_equation_set!*,"(",n,") breaks into ",
current_equation_set!*,"(",get(current_equation_set!*, 'total_used)+1,
"),...,",current_equation_set!*,"(",total_used,") by ";
maprin partial_list(polynomial_variables,5);
terpri!* nil;

setk(list(current_equation_set!*,n),0);
put(current_equation_set!*, 'total_used,total_used);
goto solved
>>

%:32%
%line 571 "integrator.web"


%:27%
%line 331 "integrator.web"
;
%34:%
%line 652 "integrator.web"

%line 653 "integrator.web"
linear_functions_list:=split_form(car df_list,
function_list);
df_list:=cdr df_list;
constants_list:=split_form(car linear_functions_list,
list get(current_equation_set!*, 'constant_operator));
linear_functions_list:=cdr linear_functions_list;
if(bracketname:=get(current_equation_set!*, 'bracketname))then
%35:%
%line 669 "integrator.web"

%line 670 "integrator.web"
if length(df_list)=0 and
length(linear_functions_list)=0 then
 <<
if atom(solvable_kernel:=
relation_analysis(!*ff2a(equation,denominator),bracketname))
then <<write current_equation_set!*,"(",n,") is a non-solvable Lie relation";
terpri!* t>>
else <<write current_equation_set!*,"(",n,") solved for ";maprin solvable_kernel;
terpri!* t;
setk(list(current_equation_set!*,n),0)>> ;
goto solved
>>

%:35%
%line 660 "integrator.web"


%:34%
%line 332 "integrator.web"
;
%36:%
%line 710 "integrator.web"

%line 711 "integrator.web"
%37:%
%line 725 "integrator.web"

%line 726 "integrator.web"
df_terms:=for each df_term in df_list join
if member(car cadr car df_term,function_list)
then list car df_term;
for each df_term in df_terms do if not member(cadr
df_term,df_functions)then df_functions:=cadr(df_term) . df_functions;
functions_and_constants_list:=append(linear_functions_list,
cdr constants_list);
linear_functions:=for each linear_function in
functions_and_constants_list collect car linear_function;
if bracketname then commutator_functions:=
get_recursive_kernels(car constants_list,
get(current_equation_set!*, 'function_list));

%:37%
%line 712 "integrator.web"
;
%38:%
%line 739 "integrator.web"

%line 740 "integrator.web"
present_variables:=variable_list;
for each variable in absent_variables do
present_variables:=delete(variable,present_variables);
nr_of_variables:=length present_variables

%:38%
%line 713 "integrator.web"
;
for each kernel in linear_functions do if length

((if depl_entry then cdr depl_entry)where depl_entry=assoc(kernel,depl!*))=nr_of_variables then
solvable_kernels:=kernel . solvable_kernels;
for each kernel in append(df_functions,commutator_functions)do
solvable_kernels:=delete(kernel,solvable_kernels);
if solvable_kernels then
%39:%
%line 745 "integrator.web"

%line 746 "integrator.web"
 <<solvable_kernel:=
find_solvable_kernel(solvable_kernels,functions_and_constants_list,denominator);
if solvable_kernel then
 <<linear_solve_and_assign(!*ff2a(equation,1),solvable_kernel);
depl!*:=
delete(assoc(solvable_kernel,depl!*),depl!*);


 <<write current_equation_set!*,"(",n,"): ","Solved for ";maprin solvable_kernel;terpri!* nil;

setk(list(current_equation_set!*,n),0);goto solved>>
>>
else
 <<write"*** ",current_equation_set!*,"(",n,"): ","Solving a function"," failed:";terpri!* t;
write"    coefficient not a number for ";
maprin
partial_list(solvable_kernels,3);terpri!* nil;
write"    Solvable with 'off coefficient_check'";
terpri!* t;goto solved>>
>>

%:39%
%line 720 "integrator.web"


%:36%
%line 333 "integrator.web"
;
%40:%
%line 772 "integrator.web"

%line 773 "integrator.web"
%41:%
%line 784 "integrator.web"

%line 785 "integrator.web"
integration_variables:=present_variables;
for each kernel in append(linear_functions,commutator_functions)do
for each variable in
((if depl_entry then cdr depl_entry)where depl_entry=assoc(kernel,depl!*))do
integration_variables:=delete(variable,integration_variables);
for each df_function in df_functions do
if not length
((if depl_entry then cdr depl_entry)where depl_entry=assoc(df_function,depl!*))=nr_of_variables then
for each variable in
((if depl_entry then cdr depl_entry)where depl_entry=assoc(df_function,depl!*))do
integration_variables:=delete(variable,integration_variables)

%:41%
%line 773 "integrator.web"
;
%43:%
%line 813 "integrator.web"

%line 814 "integrator.web"
%44:%
%line 824 "integrator.web"

%line 825 "integrator.web"
for each df_term in df_terms do
 <<if length
((if depl_entry then cdr depl_entry)where depl_entry=assoc(cadr df_term,depl!*))=nr_of_variables
and(check_differentiation_sequence(cdr cdr df_term,
integration_variables)
or member(cadr df_term,forbidden_functions))
then solvable_kernels:=if member(cadr df_term,forbidden_functions)
then list(nil,nil)else df_term . solvable_kernels;
forbidden_functions:=(cadr df_term) . forbidden_functions>> ;

%:44%
%line 814 "integrator.web"
;
%45:%
%line 834 "integrator.web"

%line 835 "integrator.web"
if solvable_kernels then
if length(solvable_kernels)=1 then
if(solvable_kernel:=find_solvable_kernel(solvable_kernels,df_list,denominator))
then
if(inhomogeneous_term:=linear_solve(mk!*sq(equation ./ 1),solvable_kernel))
and(not !*polynomial_check or
check_polynomial_integration(solvable_kernel,inhomogeneous_term))
then
 <<df_kernel:=cadr solvable_kernel;
setk(df_kernel,
inhomogeneous_integration_of(solvable_kernel,inhomogeneous_term));
depl!*:=
delete(assoc(df_kernel,depl!*),depl!*);


 <<write current_equation_set!*,"(",n,"): ","Inhomogeneous integration of ";maprin solvable_kernel;terpri!* nil;

setk(list(current_equation_set!*,n),0);goto solved>> >>
else
 <<write current_equation_set!*,"(",n,"): Inhomogeneous integration failed: ";terpri!* t;
write"inhomogeneous term not polynomial in integration variables";
terpri!* t;goto solved>>
else
 <<write"*** ",current_equation_set!*,"(",n,"): ","Inhomogeneous integration"," failed:";terpri!* t;
write"    coefficient not a number for ";
maprin
car solvable_kernels;terpri!* nil;
write"    Solvable with 'off coefficient_check'";
terpri!* t;goto solved>>
else <<write current_equation_set!*,"(",n,"): Inhomogeneous integration failed: ";terpri!* t;
write"more terms with maximal dependency";terpri!* t;goto solved>>

%:45%
%line 815 "integrator.web"


%:43%
%line 774 "integrator.web"


%:40%
%line 334 "integrator.web"
;
%51:%
%line 960 "integrator.web"

%line 961 "integrator.web"
%52:%
%line 993 "integrator.web"


present_variables:=for each variable in present_variables collect
(variable . nil . 0);

for each kernel in df_terms do
for each variable in
((if depl_entry then cdr depl_entry)where depl_entry=assoc(cadr(kernel),depl!*))do

rplacd(entry,kernel . (cddr entry+1))
where entry=assoc(variable,present_variables);;

for each kernel in linear_functions do
for each variable in
((if depl_entry then cdr depl_entry)where depl_entry=assoc(kernel,depl!*))do

rplacd(entry,kernel . (cddr entry+1))
where entry=assoc(variable,present_variables);;
if bracketname then
for each kernel in commutator_functions do
for each variable in
((if depl_entry then cdr depl_entry)where depl_entry=assoc(
kernel,depl!*))do

rplacd(entry,nil . (cddr entry+1))
where entry=assoc(variable,present_variables);

%:52%
%line 961 "integrator.web"
;
%53:%
%line 1007 "integrator.web"

%line 1008 "integrator.web"
differentiations_list:=
for each entry in present_variables join
if cadr entry and cddr entry=1 and
(polynomial_order:=get_polynomial_order(
linear_solve(mk!*sq(equation ./ 1),cadr entry),car entry))
then list(car entry . cadr entry . (polynomial_order+1));
if differentiations_list then
if !*allow_differentiation then
 <<for each entry in differentiations_list do
setk(list(current_equation_set!*,(total_used:=total_used+1)),
mk!*sq simpdf list(mk!*sq(equation ./ 1),
car entry,cddr entry));
write current_equation_set!*,"(",n,"): Generation of ",current_equation_set!*,"(",get(current_equation_set!*, 'total_used)+1,
"),...,",current_equation_set!*,"(",total_used,") by differentiation w.r.t. ";
terpri!* t;
maprin partial_list(for each entry in differentiations_list collect
list( 'list,car entry,cddr entry),10);
terpri!* nil;
put(current_equation_set!*, 'total_used,total_used);
goto solved
>>
else <<
write"*** ",current_equation_set!*,"(",n,
"): Generation of new equations by differentiation possible.";
terpri!* t;write"    Solvable with 'on allow_differentiation'";
terpri!* t;goto solved>>

%:53%
%line 962 "integrator.web"


%:51%
%line 335 "integrator.web"
;
%55:%
%line 1054 "integrator.web"

%line 1055 "integrator.web"
write current_equation_set!*,"(",n,") not solved";terpri!* t

%:55%
%line 336 "integrator.web"
;
solved:
end$

%:15%%20:%
%line 421 "integrator.web"

%line 422 "integrator.web"
lisp procedure find_solvable_kernel(kernel_list,kc_list,denominator);
if !*coefficient_check then first_solvable_kernel(kernel_list,kc_list,denominator)
else car kernel_list$


lisp procedure first_solvable_kernel(kernel_list,kc_list,denominator);
if kernel_list then
(if numberp cdr kc_pair or
numberp !*ff2a(cdr kc_pair,denominator)
then car kc_pair
else first_solvable_kernel(cdr kernel_list,kc_list,denominator))
where kc_pair=assoc(car kernel_list,kc_list)$

%:20%%21:%
%line 458 "integrator.web"

lisp procedure homogeneous_integration_of df_term;
begin scalar df_function,function_number,dependency_list,integration_list,
coefficient_name,bracketname,even_used,odd_used,
integration_variable,
number_of_integrations,solution,new_dependency_list;
%22:%
%line 483 "integrator.web"

df_function:=cadr df_term;
if not member(car df_function,get(current_equation_set!*, 'function_list))
or not fixp(function_number:=cadr df_function)or function_number=0 then

msgpri("PERFORM_HOMOGENEOUS_INTEGRATION: integration of",
df_function,"not allowed",nil,t)

%:22%
%line 465 "integrator.web"
;
dependency_list:=
((if depl_entry then cdr depl_entry)where depl_entry=assoc(df_function,depl!*));
if length dependency_list=1 then
coefficient_name:=get(current_equation_set!*, 'constant_operator)
else coefficient_name:=car df_function;
%23:%
%line 493 "integrator.web"

%line 494 "integrator.web"
if get(coefficient_name, 'rtype)= 'algebra_generator then
begin bracketname:=get(current_equation_set!*, 'bracketname);
even_used:=get(bracketname, 'even_used);
odd_used:=get(bracketname, 'odd_used);
end
else
begin
even_used:=get(coefficient_name, 'even_used);
odd_used:=get(coefficient_name, 'odd_used);
end

%:23%
%line 470 "integrator.web"
;
integration_list:=cdr cdr df_term;
%24:%
%line 507 "integrator.web"

%line 508 "integrator.web"
if integration_list then integration_variable:=car
integration_list else integration_variable:=nil;
if integration_variable and(integration_list:=cdr integration_list)
and fixp car integration_list then
 <<number_of_integrations:=car integration_list;
integration_list:=cdr integration_list>>
else number_of_integrations:=1

%:24%
%line 472 "integrator.web"
;
if bracketname then
%25:%
%line 521 "integrator.web"

%line 522 "integrator.web"
if function_number>0 then
(if even_used+number_of_integrations>get(bracketname, 'even_dimension)then
change_dimensions_of(bracketname,even_used+number_of_integrations,
get(bracketname, 'odd_dimension)))
else
(if odd_used+number_of_integrations>get(bracketname, 'odd_dimension)then
change_dimensions_of(bracketname,get(bracketname, 'even_dimension),
odd_used+number_of_integrations))

%:25%
%line 474 "integrator.web"
;
%26:%
%line 544 "integrator.web"

solution:=nil ./ 1;
while integration_variable do
begin new_dependency_list:=delete(integration_variable,dependency_list);
for i:=0:number_of_integrations-1 do
 <<solution:=addsq(solution,multsq(
if i=0 then 1 ./ 1 else mksq(integration_variable,i),
mksq(
list(coefficient_name,if function_number>0 then
(even_used:=even_used+1)else-(odd_used:=odd_used+1)),1)));
if new_dependency_list then
depl!*:=(list(coefficient_name,if function_number>0 then even_used
else-odd_used) . new_dependency_list) . depl!*;
>> ;
%24:%
%line 507 "integrator.web"

%line 508 "integrator.web"
if integration_list then integration_variable:=car
integration_list else integration_variable:=nil;
if integration_variable and(integration_list:=cdr integration_list)
and fixp car integration_list then
 <<number_of_integrations:=car integration_list;
integration_list:=cdr integration_list>>
else number_of_integrations:=1

%:24%
%line 553 "integrator.web"

end;
solution:=mk!*sq subs2 solution;

if get(coefficient_name, 'rtype)= 'algebra_generator then
define_used(bracketname,list( 'list,even_used,odd_used))
else
begin
put(coefficient_name, 'even_used,even_used);
put(coefficient_name, 'odd_used,odd_used);
end

%:26%
%line 475 "integrator.web"
;
return solution
end$

%:21%%31:%
%line 604 "integrator.web"

%line 605 "integrator.web"
lisp procedure polynomialp(expression,kernel);
if domainp expression then t
else((main_variable=kernel or not depends(main_variable,kernel))and
polynomialp(lc expression,kernel)and polynomialp(red expression,kernel))
where main_variable=mvar expression$

%:31%%33:%
%line 636 "integrator.web"

%line 637 "integrator.web"
lisp procedure partial_list(printed_list,nr_of_items);
 'list . broken_list(printed_list,nr_of_items)$

lisp procedure broken_list(list,n);
if list then if n=0 then '(!.!.!.)
else car list . broken_list(cdr list,n-1)$

%:33%%42:%
%line 806 "integrator.web"

%line 807 "integrator.web"
lisp procedure check_differentiation_sequence(sequence,variable_list);
if null sequence then t
else if fixp car sequence or
member(car sequence,variable_list)then
check_differentiation_sequence(cdr sequence,variable_list)$

%:42%%46:%
%line 863 "integrator.web"
lisp procedure check_polynomial_integration(df_term,integration_term);
%line 864 "integrator.web"
begin scalar numerator,denominator,integration_variables,variable,ok;
numerator:=numr simp integration_term;
denominator:=denr simp integration_term;
integration_variables:=
for each argument in cdr cdr df_term join
if not fixp argument then list argument;
ok:=t;
while ok and integration_variables do
 <<variable:=car integration_variables;
ok:=(not depends(denominator,variable)and polynomialp(numerator,variable));
integration_variables:=cdr integration_variables
>> ;
return ok;
end$

%:46%%47:%
%line 884 "integrator.web"

%line 885 "integrator.web"
lisp procedure inhomogeneous_integration_of(df_term,inhomogeneous_term);
begin scalar df_sequence,integration_variables,int_sequence,
variable,nr_of_integrations,integration_terms,solution,
powers,coefficient,int_factor,solution_term,n,k;
df_sequence:=cdr cdr df_term;
%48:%
%line 905 "integrator.web"

%line 906 "integrator.web"
while df_sequence do
 <<variable:=car df_sequence;
df_sequence:=cdr df_sequence;
if df_sequence and fixp car df_sequence then
 <<nr_of_integrations:=car df_sequence;
df_sequence:=cdr df_sequence>>
else nr_of_integrations:=1;
integration_variables:=variable . integration_variables;
int_sequence:=(variable . nr_of_integrations) . int_sequence
>>

%:48%
%line 890 "integrator.web"
;
integration_terms:=multi_split_form(numr simp inhomogeneous_term,
integration_variables);
integration_terms:=(nil . car integration_terms) .
cdr
integration_terms;

%49:%
%line 924 "integrator.web"

%line 925 "integrator.web"
solution:=nil ./ 1;
for each term in integration_terms do
 <<powers:=car
term;coefficient:=cdr term;
int_factor:=1;solution_term:=1 ./ 1;
for each integration in int_sequence do
 <<variable:=car integration;k:=cdr integration;
n:=(if power then cdr power else 0)where power=assoc(variable,powers);

for i:=1:k do int_factor:=(n+i)*int_factor;
solution_term:=multsq(solution_term,mksq(variable,n+k))
>> ;
solution_term:=multsq(solution_term,coefficient ./ int_factor);
solution:=addsq(solution,solution_term)
>>

%:49%
%line 896 "integrator.web"
;
solution:=multsq(solution,1 ./ denr simp inhomogeneous_term);
solution:=mk!*sq subs2 addsq(solution,simp homogeneous_integration_of df_term);
return solution
end$

%:47%%54:%
%line 1041 "integrator.web"

%line 1042 "integrator.web"
lisp procedure get_polynomial_order(expression,variable);
if not depends(denr(expression:=simp expression),variable)and
(not !*polynomial_check or polynomialp(numr expression,variable))then
begin scalar kord!*;
setkorder list !*a2k variable;
expression:=reorder numr expression;
return if mvar expression=variable then ldeg expression else 0;
end$

%:54%%56:%
%line 1063 "integrator.web"

%line 1064 "integrator.web"
algebraic procedure integrate_equations(m,n);
for i:=m:n do integrate_equation(i)$


lisp operator integrate_exceptional_equation;
lisp procedure integrate_exceptional_equation(n);
integrate_equation(n)
where
!*coefficient_check=nil,
!*polynomial_check=nil,
!*allow_differentiation=t$


%:56%%57:%
%line 1085 "integrator.web"
lisp operator show_equation;
%line 1086 "integrator.web"
lisp procedure show_equation n;
begin scalar equation,total_used,function_list;
if null(total_used:=get(current_equation_set!*, 'total_used))or
n>total_used then

msgpri("SHOW_EQUATION: properly initialize",
current_equation_set!*,nil,nil,t);
if(equation:=assoc(list(current_equation_set!*,n),get(current_equation_set!*, 'kvalue)))then
begin
equation:=setk(list(current_equation_set!*,n),aeval cadr equation);
varpri(equation,list( 'setk,mkquote list(current_equation_set!*,n),mkquote equation), 'only);
function_list:=get_recursive_kernels(numr simp equation,
get(current_equation_set!*, 'function_list));
if function_list then
 <<terpri!* t;
for each fn in function_list do
 <<maprin(fn .
((if depl_entry then cdr depl_entry)where depl_entry=assoc(fn,depl!*)));terpri!* nil>>
>>
else terpri!* nil
end
end$


algebraic procedure show_equations(m,n);
for i:=m:n do show_equation i$

%:57%%58:%
%line 1112 "integrator.web"

%line 1113 "integrator.web"
lisp operator functions_used,put_functions_used,equations_used,put_equations_used;


lisp procedure functions_used function_name;
list( 'list,get(function_name, 'even_used),get(function_name, 'odd_used))$


lisp procedure put_functions_used(function_name,even_used,odd_used);
begin
if not fixp even_used or even_used<0 or
not fixp odd_used or odd_used<0 then

msgpri("PUT_FUNCTIONS_USED: used functions number invalid",nil,nil,nil,t);
put(function_name, 'even_used,even_used);
put(function_name, 'odd_used,odd_used);
end$


lisp procedure equations_used;
get(current_equation_set!*, 'total_used)$


lisp procedure put_equations_used(n);
if not fixp n or n<0 then

msgpri("PUT_EQUATIONS_USED: used equation number invalid",nil,nil,nil,t)
else put(current_equation_set!*, 'total_used,n)$

%:58%%59:%
%line 1149 "integrator.web"

%line 1150 "integrator.web"
lisp operator df_acts_as_derivation_on;

lisp procedure df_acts_as_derivation_on operator_name;
begin
put(operator_name, 'dfform, 'df_as_derivation);
end$

%:59%%60:%
%line 1161 "integrator.web"

%line 1162 "integrator.web"
lisp procedure df_as_derivation(kernel,variable,power);
begin scalar left_part,right_part,argument,derivative;
if power neq 1 then

msgpri("DF_AS_DERIVATION:",kernel,"must occur linearly",nil,t);
left_part:=list car kernel;right_part:=cdr kernel;
derivative:=nil . 1;
while right_part do
 <<argument:=car right_part;right_part:=cdr right_part;
derivative:=addsq(derivative,
simp append(reverse left_part,list( 'df,argument,variable) . right_part));
left_part:=argument . left_part;
>> ;
return derivative;
end$

%:60%%62:%
%line 1191 "integrator.web"

%line 1192 "integrator.web"
lisp operator listlength$
lisp procedure listlength l;
listpri_depth!*:=l$

%:62%%63:%
%line 1200 "integrator.web"

%line 1201 "integrator.web"
symbolic procedure listpri l;
begin scalar orig,split,u;
u:=l;
l:=cdr l;
prin2!* get( '!*lcbkt!*, 'prtch);

orig:=orig!*;
orig!*:=if posn!*<18 then posn!* else orig!*+3;
if null l then go to b;
split:=treesizep(l,listpri_depth!*);
a:maprint(negnumberchk car l,0);
l:=cdr l;
if null l then go to b;
oprin '!*comma!*;
if split then terpri!* t;
go to a;
b:prin2!* get( '!*rcbkt!*, 'prtch);
orig!*:=orig;
return u
end$

%:63%%64:%
%line 1224 "integrator.web"
end;
%line 1225 "integrator.web"

%:64%