begin support for integrals

Author: dqnykamp

lib/converters/ast-to-latex.js

@@ -172,7 +172,7 @@ const operators = {
 
 // allowed multicharacter latex symbols
 // in addition to the below applied function symbols
-const allowedLatexSymbolsDefault = ['alpha', 'beta', 'gamma', 'Gamma', 'delta', 'Delta', 'epsilon', 'zeta', 'eta', 'theta', 'Theta', 'iota', 'kappa', 'lambda', 'Lambda', 'mu', 'nu', 'xi', 'Xi', 'pi', 'Pi', 'rho', 'sigma', 'Sigma', 'tau', 'Tau', 'upsilon', 'Upsilon', 'phi', 'Phi', 'chi', 'psi', 'Psi', 'omega', 'Omega', 'partial', "abs", "exp", "log", "ln", "log10", "sign", "sqrt", "erf", "cos", "cosh", "cot", "coth", "csc", "csch", "sec", "sech", "sin", "sinh", "tan", "tanh", 'arcsin', 'arccos', 'arctan', 'arccsc', 'arcsec', 'arccot', 'arg', 'Re', 'Im', 'det', 'angle', 'perp', 'circ'];
+const allowedLatexSymbolsDefault = ['alpha', 'beta', 'gamma', 'Gamma', 'delta', 'Delta', 'epsilon', 'zeta', 'eta', 'theta', 'Theta', 'iota', 'kappa', 'lambda', 'Lambda', 'mu', 'nu', 'xi', 'Xi', 'pi', 'Pi', 'rho', 'sigma', 'Sigma', 'tau', 'Tau', 'upsilon', 'Upsilon', 'phi', 'Phi', 'chi', 'psi', 'Psi', 'omega', 'Omega', 'partial', "abs", "exp", "log", "ln", "log10", "sign", "sqrt", "erf", "cos", "cosh", "cot", "coth", "csc", "csch", "sec", "sech", "sin", "sinh", "tan", "tanh", 'arcsin', 'arccos', 'arctan', 'arccsc', 'arcsec', 'arccot', 'arg', 'Re', 'Im', 'det', 'angle', 'perp', 'circ', 'int'];
 
 
 const convertLatexSymbolsDefault = {
@@ -656,20 +656,59 @@ class astToLatex {
         return '\\left\\lfloor ' + this.statement(operands[1]) + ' \\right\\rfloor';
       } else if (operands[0] === 'ceil') {
         return '\\left\\lceil ' + this.statement(operands[1]) + ' \\right\\rceil';
-      }
-
-      if (operands[0] === "factorial") {
+      } else if (operands[0] === "factorial") {
         let result = this.factor(operands[1]);
         if (this.simple_factor_or_function_or_parens(operands[1]) ||
           (operands[1][0] === '_' && (typeof operands[1][1] === 'string'))
         )
           return result + "!";
         else
           return '\\left(' + result + '\\right)!';
+      } else if (operands[0] === 'sqrt') {
+        return '\\sqrt{' + this.statement(operands[1]) + '}';
       }
 
-      if (operands[0] === 'sqrt') {
-        return '\\sqrt{' + this.statement(operands[1]) + '}';
+
+      // check if have integral
+      let fun = operands[0];
+      if (fun[0] === "^") {
+        fun = fun[1];
+      }
+      if (fun[0] === "_") {
+        fun = fun[1]
+      }
+      if (fun === "int") {
+        let integral = this.factor(operands[0]);
+        let integrand_ast = operands[1];
+        let integrand;
+        if (Array.isArray(integrand_ast) && integrand_ast[0] === "*") {
+          let ds = [];
+          let integrand_ast2 = ["*"];
+          for (let i = 1; i < integrand_ast.length; i++) {
+            let factor = integrand_ast[i];
+            if (Array.isArray(factor) && factor[0] === "d") {
+              ds.push(factor);
+            } else {
+              integrand_ast2.push(factor);
+            }
+          }
+
+          integrand = this.term(integrand_ast2);
+
+          if (ds.length > 0) {
+
+            if (integrand[integrand.length - 1].match(/[a-zA-Z]/)) {
+              integrand += "\\,"
+            }
+            integrand += ds.map(x => "d" + this.factor(x[1])).join("\\,")
+          }
+        }
+
+        if (!integrand) {
+          integrand = this.term(operands[1]);
+        }
+
+        return integral + ' ' + integrand;
       }
 
       let f;

lib/converters/ast-to-text.js

@@ -380,6 +380,7 @@ class astToText {
       'Omega': 'Ω',
       'omega': 'ω',
       'perp': '⟂',
+      'int': '∫',
     }
     if (this.output_unicode && (symbol in symbolConversions)) {
       return symbolConversions[symbol];
@@ -664,9 +665,7 @@ class astToText {
 
       if (operands[0] === 'abs') {
         return '|' + this.statement(operands[1]) + '|';
-      }
-
-      if (operands[0] === "factorial") {
+      } else if (operands[0] === "factorial") {
         let result = this.factor(operands[1]);
         if (this.simple_factor_or_function_or_parens(operands[1]) ||
           (operands[1][0] === '_' && (typeof operands[1][1] === 'string'))
@@ -677,6 +676,45 @@ class astToText {
 
       }
 
+
+      // check if have integral
+      let fun = operands[0];
+      if (fun[0] === "^") {
+        fun = fun[1];
+      }
+      if (fun[0] === "_") {
+        fun = fun[1]
+      }
+      if (fun === "int") {
+        let integral = this.factor(operands[0]);
+        let integrand_ast = operands[1];
+        let integrand;
+        if (Array.isArray(integrand_ast) && integrand_ast[0] === "*") {
+          let ds = [];
+          let integrand_ast2 = ["*"];
+          for (let i = 1; i < integrand_ast.length; i++) {
+            let factor = integrand_ast[i];
+            if (Array.isArray(factor) && factor[0] === "d") {
+              ds.push(factor);
+            } else {
+              integrand_ast2.push(factor);
+            }
+          }
+
+          integrand = this.term(integrand_ast2);
+
+          if (ds.length > 0) {
+            integrand += " " + ds.map(x => "d" + this.factor(x[1])).join(" ")
+          }
+        }
+
+        if (!integrand) {
+          integrand = this.term(operands[1]);
+        }
+
+        return integral + ' ' + integrand;
+      }
+
       let f = this.factor(operands[0]);
       let f_args = this.statement(operands[1]);
 

lib/converters/latex-to-ast.js

@@ -325,6 +325,8 @@ const base_latex_rules = [
 
   ['\\\\angle(?![a-zA-Z])', 'ANGLE'],
 
+  ['\\\\int(?![a-zA-Z])', 'INT'],
+
   ['!', '!'],
   ['\'', '\''],
   ['_', '_'],
@@ -1485,6 +1487,46 @@ class latexToAst {
           result = ["angle", ...args];
         }
       }
+    } else if (this.token.token_type === 'INT') {
+
+      this.advance();
+
+      let result = "int";
+
+
+      if (this.token.token_type === "_") {
+        this.advance();
+        let subscript = this.get_subsuperscript({ parse_absolute_value });
+        result = ['_', result, subscript];
+      }
+
+      if (this.token.token_type === '^') {
+        this.advance();
+        let superscript = this.get_subsuperscript({ parse_absolute_value });
+        result = ["^", result, superscript];
+      }
+
+      let integrand = flatten(this.term({ parse_absolute_value }));
+
+      if (Array.isArray(integrand) && integrand[0] === "*") {
+        // look for consecutive factors of "d" followed by a string
+
+        let ds = [];
+        for (let i = 0; i < integrand.length - 1; i++) {
+          let factor1 = integrand[i];
+          if (factor1 === "d") {
+            let factor2 = integrand[i + 1];
+            integrand.splice(i, 2);
+            ds.push(["d", factor2]);
+            i--;
+          }
+        }
+        integrand.push(...ds);
+
+      }
+
+      return ["apply", result, integrand];
+
     }
 
     if (this.token.token_type === '_') {

lib/converters/text-to-ast.js

@@ -334,6 +334,9 @@ const base_text_rules = [
   ['angle\\b', 'ANGLE'],
   ['\u2220', 'ANGLE'],  // '∠'
 
+  ['int(?![a-zA-Z])', 'INT'],
+  ['\u222b', 'INT'],  // '∫'
+
   ['!', '!'],
   ['\'', '\''],
   ['_', '_'],
@@ -1264,8 +1267,47 @@ class textToAst {
           result = ["angle", ...args];
         }
       }
-    }
+    } else if (this.token.token_type === 'INT') {
+
+      this.advance();
+
+      let result = "int";
+
+
+      if (this.token.token_type === "_") {
+        this.advance();
+        let subscript = this.get_subsuperscript({ parse_absolute_value });
+        result = ['_', result, subscript];
+      }
+
+      if (this.token.token_type === '^') {
+        this.advance();
+        let superscript = this.get_subsuperscript({ parse_absolute_value });
+        result = ["^", result, superscript];
+      }
+
+      let integrand = flatten(this.term({ parse_absolute_value }));
 
+      if (Array.isArray(integrand) && integrand[0] === "*") {
+        // look for consecutive factors of "d" followed by a string
+
+        let ds = [];
+        for (let i = 0; i < integrand.length - 1; i++) {
+          let factor1 = integrand[i];
+          if (factor1 === "d") {
+            let factor2 = integrand[i + 1];
+            integrand.splice(i, 2);
+            ds.push(["d", factor2]);
+            i--;
+          }
+        }
+        integrand.push(...ds);
+
+      }
+
+      return ["apply", result, integrand];
+
+    }
 
 
     if (this.token.token_type === '_') {

spec/quick_latex-to-ast-to-latex.spec.js

@@ -319,6 +319,11 @@ var inputs = [
   ['x 50 \\circ y', '(x \\cdot 50 \\circ) y'],
   ['x$8y', 'x($8y)'],
   ['x 75%y', '(x \\cdot 75%)y'],
+  ['\\int_a^bf(x)dx', '\\int_{a}^{b}f(x)dx'],
+  '\\int f(x) dx',
+  ['\\int x^2 dx', '\\int x^{2} dx'],
+  ['\\int (x^2+y^2)dxdy', '\\int (x^{2}+y^{2})dxdy'],
+  ['\\int dx f(x)', '\\int f(x) dx'],
 ];
 
 function clean(text) {

spec/quick_text-to-ast-to-text.spec.js

@@ -320,6 +320,11 @@ var inputs = [
   ['x 50deg y', '(x*50 deg) y'],
   ['x$8y', 'x($8y)'],
   ['x 75%y', '(x*75%)y'],
+  ['int_a^bf(x)dx', '∫_a^bf(x)dx'],
+  ['int f(x)dx', '∫f(x)dx'],
+  ['int x^2 dx', '∫x^2 dx'],
+  ['int (x^2+y^2)dxdy', '∫(x^2+y^2)dxdy'],
+  ['int dx f(x)', '∫f(x) dx'],
 ];
 
 

spec/slow_math-expressions.spec.js

@@ -382,6 +382,10 @@ describe("expression", function () {
     ['50% + 1', '1.5'],
     ['x%', 'x/100'],
     ['180 deg', 'pi'],
+    ['∫_(a+a)^(5b-b)xx dx', '∫_(2a)^(4b)x^2dx'],
+    ['∫_(a+a)^(5b-b)dx xx', '∫_(2a)^(4b)x^2dx'],
+    ['∫ f(x)f(x)dx', '∫ f(x)^2dx'],
+
   ];
 
   _.each(equivalences, function (equiv) {
@@ -477,6 +481,11 @@ describe("expression", function () {
     ['∠ABC', '∠ACB'],
     ['$5', '5'],
     ['$x', 'x'],
+    ['∫_a^b xdx', '∫_(2a)^b xdx'],
+    ['∫_a^b xdx', '∫_a^(2b) xdx'],
+    ['∫_a^b xdx', '∫_a^b 2xdx'],
+    ['∫ xdx', '∫ 2xdx'],
+    ['∫ f(x)dx', '∫ g(x)dx'],
   ];
 
   _.each(nonequivalences, function (nonequiv) {