SYMBOLICDIFF

A Prolog - C project to implement symbolic differentiation. The front end is built in C while the actual derivation is performed in Prolog.

Requirements

SWI-Prolog is needed. Installation manual: https://www.swi-prolog.org/build/unix.html Currently, SWI prolog is called through a system call (execlp). In the future, it would be nice to use its C API.

Building

cd src
make

Function/predicates available

Without steps:

differentiate(Formula,Variable(s))
gradient(Formula)
jacobian(Formula) (still not implemented)
hessian(Formula) (still not implemented)

With steps:

differentiate_steps(Formula,Variable(s))
gradient_steps(Formula)
jacobian_steps(Formula) (still not implemented)
hessian_steps(Formula) (still not implemented)

Command Line Options

Usage: symdiff [OPTION...] EQUATION
SYMDIFF -- symbolic derivative and more
example: symdiff 3*x^2 -d x
nexample: symdiff 3*x^2 + y -d [x,y]

  -e, --evaluate             Evaluate the derivative
  -p, --print-steps          Print derivation steps
  -g, --gradient             Compute the gradient 
  -H, --hessian              Compute Hessian matrix
  -j, --jacobian             Compute Jacobian matrix
  -t, --tex                  Print latex output
  -i, --interactive          Interactive mode
  -?, --help                 Give this help list
  -d, --derivate=VARIABLE(s) Compute derivative w.r.t. VARIABLE(s)
  -o, --output=FILE          Output to FILE instead of standard output
  -q, --quiet                Don't produce any output
      --usage                Give a short usage message
  -v, --verbose              Produce verbose output
  -V, --version              Print program version

Report bugs to <github_issue>.

Examples

Symbolic differentiate:

./symdiff 3*x+4*y+5*z -d x
x: 3*1+4*0+5*0

./symdiff 3*x+4*y+5*z -d [x,y,z]
dx: 3*1+4*0+5*0
dy: 3*0+4*1+5*0
dz: 3*0+4*0+5*1

Gradient:

./symdiff 3*x+4*y+5*z -g
dx: 3*1+4*0+5*0
dy: 3*0+4*1+5*0
dz: 3*0+4*0+5*1

Evaluate the function:

./symdiff 3*x+4*y+5*z -e [[x,1],[y,2],[z,3]]
26

Evaluate the derivative(s):

./symdiff 3*x+4*y+5*z -d [x,y,z] -e [[x,1],[y,2],[z,3]]
[3,4,5]

Print steps:

./symdiff 3*x+4*y+5*z -d x -p
dx: 3*1+4*0+5*0
[sum_rule,sum_rule,constant*function,one_variable,constant*function,one_variable,constant*function,one_variable]
[(d/d(x:3*x+4*y+5*z)->3*1+4*0+5*0),(d/d(x:3*x+4*y)->3*1+4*0),(d/d(x:3*x)->3*1),(d/d(x:x)->1),(d/d(x:4*y)->4*0),(d/d(x:y)->0),(d/d(x:5*z)->5*0),(d/d(x:z)->0)]

./symdiff 3*x+4*y+5*z -d [x,y] -p
dx: 3*1+4*0+5*0
[sum_rule,sum_rule,constant*function,one_variable,constant*function,one_variable,constant*function,one_variable]
[(d/d(x:3*x+4*y+5*z)->3*1+4*0+5*0),(d/d(x:3*x+4*y)->3*1+4*0),(d/d(x:3*x)->3*1),(d/d(x:x)->1),(d/d(x:4*y)->4*0),(d/d(x:y)->0),(d/d(x:5*z)->5*0),(d/d(x:z)->0)]
dy: 3*0+4*1+5*0
[sum_rule,sum_rule,constant*function,one_variable,constant*function,one_variable,constant*function,one_variable]
[(d/d(y:3*x+4*y+5*z)->3*0+4*1+5*0),(d/d(y:3*x+4*y)->3*0+4*1),(d/d(y:3*x)->3*0),(d/d(y:x)->0),(d/d(y:4*y)->4*1),(d/d(y:y)->1),(d/d(y:5*z)->5*0),(d/d(y:z)->0)]

Return Values

See src/errors.h:

FORK_ERROR_EXIT -2
PIPE_ERROR_EXIT -3
EXECLP_ERROR_EXIT -4
FOPEN_ERROR_EXIT -5
EXEC_NULL_ERROR_EXIT -6

C API Example

You can find the following example in the folder test

#include <stdio.h>
#include "../src/symdiff.h"

int main() {
    printf("%s\n",evaluate_expr("3*x+4*y+5*z","[[x,1],[y,2],[z,3]]"));
    return 0;
}

Compile it with gcc test_c_api.c -L../src/ -lsymdiff -Wl,-rpath,../src/ Then run it with ./a.out.

Repository Structure

.
├── include
│   └── symdiff.h -> symdiff.h
├── README.md
├── src
│   ├── compile.sh
│   ├── differentiate.pl
│   ├── errors.h
│   ├── main.c
│   ├── Makefile
│   ├── parser.c
│   ├── parser.h
│   ├── symdiff
│   ├── symdiff.c
│   ├── symdiff.h
└── test
    ├── test_c_api.c
    └── test.pl

Future Steps

Dynamic memory allocation, especially in reading from pipe
Read functions from file
Interface (GUI)
Print latex format
Plot the functions

damianoazzolini/symbolicdiff