trig identities part 2

together-science · Sep 20, 2024 · 49e1e7b · 49e1e7b
1 parent cb91dfa
commit 49e1e7b
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Showing 5 changed files with 54 additions and 41 deletions.
diff --git a/Algebra.js b/Algebra.js
@@ -4352,42 +4352,57 @@ if((typeof module) !== 'undefined') {
                     }
                     else if((symbol.fname === 'cos' || symbol.fname === 'sin') &&
                             (symbol.args[0].group == CP)) {
-
-                            // capture cos(x-pi/2) => sin(x) and sin(x+pi/2) = cos(x)
-                            // but generalized
-                            // test the sum for presence of a "n*pi/2" summands
-                            let count = 0;
-                            let newArg = new Symbol(0);
-                            let piOverTwo = _.parse('pi/2');
-                            symbol.args[0].each((x)=>{
-                                let c = _.divide(x.clone(), piOverTwo.clone());
-                                c = __.Simplify._simplify(c);
-                                c = core.Utils.evaluate(c);
-                                if (isInt(c)) {
-                                    count += c.multiplier.num.value;
-                                } else {
-                                    newArg = _.add(newArg, x);
-                                }
-                            });
-                            if (count) {
-                                count = count % 4;
-                                count += (count < 0)?4:0;
-                                count += (symbol.fname === 'cos')?1:0;
-                                // console.log(count);
-                                // debugger;
-                                const results = [
-                                    "sin({0})",
-                                    "cos({0})",
-                                    "-sin({0})",
-                                    "-cos({0})",
-                                ];
-                                const s = core.Utils.format(results[count], newArg);
-                                retval = _.parse(s);
-                                workDone = true;
+                        // capture cos(x-pi/2) => sin(x) and sin(x+pi/2) = cos(x)
+                        // but generalized
+                        // test the sum for presence of a "n*pi/2" summands
+                        let count = 0;
+                        let newArg = new Symbol(0);
+                        let piOverTwo = _.parse('pi/2');
+                        symbol.args[0].each((x)=>{
+                            let c = _.divide(x.clone(), piOverTwo.clone());
+                            c = __.Simplify._simplify(c);
+                            c = core.Utils.evaluate(c);
+                            if (isInt(c)) {
+                                count += c.multiplier.num.value;
+                            } else {
+                                newArg = _.add(newArg, x);
                             }
-
+                        });
+                        if (count) {
+                            count += (symbol.fname === 'cos')?1:0;
+                            count = count % 4;
+                            count += (count < 0)?4:0;
+                            // console.log(count);
+                            // debugger;
+                            const results = [
+                                "sin({0})",
+                                "cos({0})",
+                                "-sin({0})",
+                                "-cos({0})",
+                            ];
+                            const s = core.Utils.format(results[count], newArg);
+                            retval = _.parse(s);
+                            workDone = true;
+                        } else if (Object.keys(symbol.args[0].symbols).length > 1) {
+                            // apply sin(a+-b) => sin(a)cos(b)+-cos(a)sin(b)
+                            //   and cos(a+-b) => cos(a)cos(b)-+sin(a)sin(b)
+                            const arg = symbol.args[0].clone();
+                            const summands = Object.values(arg.symbols);
+                            const a = summands[0];
+                            const b = summands.slice(1);
+                            const bStr = b.map((x)=>"("+x.text()+")").join("+");
+                            let s;
+                            if (symbol.fname === 'sin') {
+                                s = core.Utils.format("sin({0})cos({1})+sin({1})cos({0})", a, bStr);
+                            } else {
+                                s = core.Utils.format("cos({0})cos({1})-sin({1})sin({0})", a, bStr);
+                            }
+                            retval = _.parse(s);
+                            workDone = true;
+                        }
                     } else if((symbol.fname === 'cos' || symbol.fname === 'sin') &&
                             (symbol.args[0].multiplier.sign() == -1)) {
+                        // sin(-x) => -sin(x), cos(-x) => cos(x)
                         // remove the minus from the argument
                         const newArg = symbol.args[0].clone().negate();
                         // make the new trig call
@@ -4401,6 +4416,7 @@ if((typeof module) !== 'undefined') {
                     } if(symbol.fname === 'sin' &&
                         symbol.args[0].multiplier.equals(2) &&
                         !symbol.args[0].equals(2)) {
+                        // sin(2x) => 2sin(x)cos(x)
                         // remove the minus from the argument
                         const newArg = symbol.args[0].clone().toUnitMultiplier();
                         // make the new trig call
@@ -4410,8 +4426,6 @@ if((typeof module) !== 'undefined') {
                         workDone = true;
                     }
 
-
-
                     retval = __.Simplify.unstrip(sym_array, retval).distributeMultiplier();
                     symbol = retval;
                     if (iterations > 10) {

diff --git a/all.min.js b/all.min.js
diff --git a/package.json b/package.json
@@ -6,7 +6,7 @@
     "description": "javascript light-weight symbolic math library",
     "name": "nerdamer-prime",
     "license": "MIT",
-    "version": "1.1.23",
+    "version": "1.1.24",
     "homepage": "https://github.com/together-science/nerdamer-prime",
     "directory": {
         "lib": "./"

diff --git a/spec/algebra.spec.js b/spec/algebra.spec.js
@@ -369,9 +369,8 @@ describe('Algebra', function () {
 
         expect(nerdamer('simplify(tan(x)-sin(x)/cos(x))').toString()).toEqual('0')
 
-        // todo:
-        // expect(nerdamer('simplify(sin(x+y)-(sin(x)*cos(y)+cos(x)*sin(y)))').toString()).toEqual('0')
-        // expect(nerdamer('simplify(cos(x+y)-(cos(x)*cos(y)-sin(x)*sin(y)))').toString()).toEqual('0')
+        expect(nerdamer('simplify(sin(x+y)-(sin(x)*cos(y)+cos(x)*sin(y)))').toString()).toEqual('0')
+        expect(nerdamer('simplify(cos(x+y)-(cos(x)*cos(y)-sin(x)*sin(y)))').toString()).toEqual('0')
     });
 
     it('regression tests', function() {

diff --git a/spec/test.js b/spec/test.js
@@ -44,7 +44,7 @@ try {
     // console.log(x.text());
     // return;
     // x= nerdamer("-sqrt(8/12)")
-    x= nerdamer("limit(tan(3*x)/tan(x), x, pi/2)");
+    x= nerdamer("simplify(cos(a+b))");
     console.log(x.text());
 } catch (error) {
     console.log("error "+error)