feat: add Calculator & Grapher tool

Adds a full-featured mathematical calculator and interactive function
grapher at /calculate. Powered by Math.js v15 with a HiDPI Canvas
renderer for the graph.

- Evaluates arbitrary math expressions (trig, log, complex, matrices,
  factorials, combinatorics, and more) with named variable scope
- Persists history (50 entries) and variables via localStorage
- 32 quick-insert buttons for constants and functions
- Interactive graph: pan (drag), zoom (scroll), crosshair tooltip
  showing cursor coords and f₁(x)…f₈(x) values simultaneously
- Up to 8 color-coded functions with inline color pickers and
  visibility toggles
- Discontinuity detection for functions like tan(x)
- Adaptive grid labels that rescale with zoom
- Responsive layout: 2/5–3/5 split on desktop, tabbed on mobile

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

pnpm-lock.yaml

@@ -56,6 +56,9 @@ importers:
       lucide-react:
         specifier: ^0.575.0
         version: 0.575.0(react@19.2.4)
+      mathjs:
+        specifier: ^15.1.1
+        version: 15.1.1
       next:
         specifier: ^16.1.6
         version: 16.1.6(@babel/core@7.29.0)(react-dom@19.2.4(react@19.2.4))(react@19.2.4)
@@ -257,6 +260,10 @@ packages:
     peerDependencies:
       '@babel/core': ^7.0.0-0
 
+  '@babel/runtime@7.28.6':
+    resolution: {integrity: sha512-05WQkdpL9COIMz4LjTxGpPNCdlpyimKppYNoJ5Di5EUObifl8t4tuLuUBBZEpoLYOmfvIWrsp9fCl0HoPRVTdA==}
+    engines: {node: '>=6.9.0'}
+
   '@babel/template@7.28.6':
     resolution: {integrity: sha512-YA6Ma2KsCdGb+WC6UpBVFJGXL58MDA6oyONbjyF/+5sBgxY/dwkhLogbMT2GXXyU84/IhRw/2D1Os1B/giz+BQ==}
     engines: {node: '>=6.9.0'}
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     engines: {node: '>=20'}
 
+  complex.js@2.4.3:
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+
   concat-map@0.0.1:
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     engines: {node: '>=0.10.0'}
 
+  decimal.js@10.6.0:
+    resolution: {integrity: sha512-YpgQiITW3JXGntzdUmyUR1V812Hn8T1YVXhCu+wO3OpS4eU9l4YdD3qjyiKdV6mvV29zapkMeD390UVEf2lkUg==}
+
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     peerDependencies:
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+  escape-latex@1.2.0:
+    resolution: {integrity: sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw==}
+
   escape-string-regexp@4.0.0:
     resolution: {integrity: sha512-TtpcNJ3XAzx3Gq8sWRzJaVajRs0uVxA2YAkdb1jm2YkPz4G6egUFAyA3n5vtEIZefPk5Wa4UXbKuS5fKkJWdgA==}
     engines: {node: '>=10'}
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     engines: {node: '>= 0.6'}
 
+  fraction.js@5.3.4:
+    resolution: {integrity: sha512-1X1NTtiJphryn/uLQz3whtY6jK3fTqoE3ohKs0tT+Ujr1W59oopxmoEh7Lu5p6vBaPbgoM0bzveAW4Qi5RyWDQ==}
+
   framer-motion@12.34.3:
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     peerDependencies:
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     engines: {node: '>= 0.4'}
 
+  javascript-natural-sort@0.7.1:
+    resolution: {integrity: sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw==}
+
   jiti@2.6.1:
     resolution: {integrity: sha512-ekilCSN1jwRvIbgeg/57YFh8qQDNbwDb9xT/qu2DAHbFFZUicIl4ygVaAvzveMhMVr3LnpSKTNnwt8PoOfmKhQ==}
     hasBin: true
@@ -3051,6 +3073,11 @@ packages:
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     engines: {node: '>= 0.4'}
 
+  mathjs@15.1.1:
+    resolution: {integrity: sha512-rM668DTtpSzMVoh/cKAllyQVEbBApM5g//IMGD8vD7YlrIz9ITRr3SrdhjaDxcBNTdyETWwPebj2unZyHD7ZdA==}
+    engines: {node: '>= 18'}
+    hasBin: true
+
   media-typer@1.1.0:
     resolution: {integrity: sha512-aisnrDP4GNe06UcKFnV5bfMNPBUw4jsLGaWwWfnH3v02GnBuXX2MCVn5RbrWo0j3pczUilYblq7fQ7Nw2t5XKw==}
     engines: {node: '>= 0.8'}
@@ -3558,6 +3585,9 @@ packages:
   scheduler@0.27.0:
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+  seedrandom@3.0.5:
+    resolution: {integrity: sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg==}
+
   semver@6.3.1:
     resolution: {integrity: sha512-BR7VvDCVHO+q2xBEWskxS6DJE1qRnb7DxzUrogb71CWoSficBxYsiAGd+Kl0mmq/MprG9yArRkyrQxTO6XjMzA==}
     hasBin: true
@@ -3773,6 +3803,9 @@ packages:
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     engines: {node: '>=6'}
 
+  tiny-emitter@2.1.0:
+    resolution: {integrity: sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q==}
+
   tiny-invariant@1.3.3:
     resolution: {integrity: sha512-+FbBPE1o9QAYvviau/qC5SE3caw21q3xkvWKBtja5vgqOWIHHJ3ioaq1VPfn/Szqctz2bU/oYeKd9/z5BL+PVg==}
 
@@ -3853,6 +3886,10 @@ packages:
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     engines: {node: '>= 0.4'}
 
+  typed-function@4.2.2:
+    resolution: {integrity: sha512-VwaXim9Gp1bngi/q3do8hgttYn2uC3MoT/gfuMWylnj1IeZBUAyPddHZlo1K05BDoj8DYPpMdiHqH1dDYdJf2A==}
+    engines: {node: '>= 18'}
+
   typescript@5.9.3:
     resolution: {integrity: sha512-jl1vZzPDinLr9eUt3J/t7V6FgNEw9QjvBPdysz9KfQDD41fQrC2Y4vKQdiaUpFT4bXlb1RHhLpp8wtm6M5TgSw==}
     engines: {node: '>=14.17'}
@@ -4218,6 +4255,8 @@ snapshots:
     transitivePeerDependencies:
       - supports-color
 
+  '@babel/runtime@7.28.6': {}
+
   '@babel/template@7.28.6':
     dependencies:
       '@babel/code-frame': 7.29.0
@@ -5911,6 +5950,8 @@ snapshots:
 
   commander@14.0.3: {}
 
+  complex.js@2.4.3: {}
+
   concat-map@0.0.1: {}
 
   content-disposition@1.0.1: {}
@@ -5988,6 +6029,8 @@ snapshots:
 
   decamelize@1.2.0: {}
 
+  decimal.js@10.6.0: {}
+
   dedent@1.7.1: {}
 
   deep-is@0.1.4: {}
@@ -6172,6 +6215,8 @@ snapshots:
 
   escape-html@1.0.3: {}
 
+  escape-latex@1.2.0: {}
+
   escape-string-regexp@4.0.0: {}
 
   eslint-config-next@15.1.7(eslint@9.39.3(jiti@2.6.1))(typescript@5.9.3):
@@ -6538,6 +6583,8 @@ snapshots:
 
   forwarded@0.2.0: {}
 
+  fraction.js@5.3.4: {}
+
   framer-motion@12.34.3(react-dom@19.2.4(react@19.2.4))(react@19.2.4):
     dependencies:
       motion-dom: 12.34.3
@@ -6883,6 +6930,8 @@ snapshots:
       has-symbols: 1.1.0
       set-function-name: 2.0.2
 
+  javascript-natural-sort@0.7.1: {}
+
   jiti@2.6.1: {}
 
   jose@6.1.3: {}
@@ -7124,6 +7173,18 @@ snapshots:
 
   math-intrinsics@1.1.0: {}
 
+  mathjs@15.1.1:
+    dependencies:
+      '@babel/runtime': 7.28.6
+      complex.js: 2.4.3
+      decimal.js: 10.6.0
+      escape-latex: 1.2.0
+      fraction.js: 5.3.4
+      javascript-natural-sort: 0.7.1
+      seedrandom: 3.0.5
+      tiny-emitter: 2.1.0
+      typed-function: 4.2.2
+
   media-typer@1.1.0: {}
 
   merge-descriptors@2.0.0: {}
@@ -7704,6 +7765,8 @@ snapshots:
 
   scheduler@0.27.0: {}
 
+  seedrandom@3.0.5: {}
+
   semver@6.3.1: {}
 
   semver@7.7.4: {}
@@ -8015,6 +8078,8 @@ snapshots:
 
   tapable@2.3.0: {}
 
+  tiny-emitter@2.1.0: {}
+
   tiny-invariant@1.3.3: {}
 
   tinyexec@1.0.2: {}
@@ -8113,6 +8178,8 @@ snapshots:
       possible-typed-array-names: 1.1.0
       reflect.getprototypeof: 1.0.10
 
+  typed-function@4.2.2: {}
+
   typescript@5.9.3: {}
 
   unbox-primitive@1.1.0: