NTT-learning/notebooks/foundations/01_convolution_to_toy_ntt/studio.ipynb

{
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      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "theme",
          "title": "Notebook Theme"
        }
      },
      "source": "## META\n\n<style>\n.jp-RenderedHTMLCommon h2 {\n  display: none;\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-head {\n  position: relative;\n  margin: 0 0 0.8rem 0;\n  padding: 0.95rem 1rem 0.95rem 1rem;\n  border-radius: 16px;\n  border: 1px solid rgba(16,42,67,0.12);\n  box-shadow: 0 8px 24px rgba(16,42,67,0.06);\n  font-family: \"Avenir Next\", \"Trebuchet MS\", sans-serif;\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-row {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 0.45rem;\n  align-items: center;\n  margin-bottom: 0.55rem;\n}\n\n.jp-RenderedHTMLCommon .ntt-role-pill,\n.jp-RenderedHTMLCommon .ntt-kind-pill,\n.jp-RenderedHTMLCommon .ntt-difficulty-pill {\n  display: inline-flex;\n  align-items: center;\n  padding: 0.18rem 0.58rem;\n  border-radius: 999px;\n  font-size: 0.72rem;\n  font-weight: 800;\n  letter-spacing: 0.04em;\n  text-transform: uppercase;\n}\n\n.jp-RenderedHTMLCommon .ntt-role-meta {\n  background: linear-gradient(135deg, #e2f3ff 0%, #f5fbff 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-mandatory {\n  background: linear-gradient(135deg, #fff0b3 0%, #ffd58a 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-facultative {\n  background: linear-gradient(135deg, #ffe1d6 0%, #ffc9b9 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-pill {\n  color: #102a43;\n  background: rgba(16,42,67,0.1);\n}\n\n.jp-RenderedHTMLCommon .ntt-kind-pill {\n  color: #486581;\n  background: rgba(255,255,255,0.72);\n}\n\n.jp-RenderedHTMLCommon .ntt-difficulty-pill {\n  position: absolute;\n  top: 0.95rem;\n  right: 1rem;\n  color: #102a43;\n  background: rgba(255,255,255,0.88);\n  border: 1px solid rgba(16,42,67,0.08);\n  box-shadow: 0 4px 12px rgba(16,42,67,0.08);\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-title {\n  font-size: 1.25rem;\n  line-height: 1.25;\n  font-weight: 850;\n  color: #102a43;\n  padding-right: 5.3rem;\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-body-hint {\n  margin-top: 0.3rem;\n  font-size: 0.84rem;\n  color: #486581;\n}\n\n.jupyter-widgets.widget-container,\n.jupyter-widgets.widget-box,\n.jupyter-widgets.widget-vbox,\n.jupyter-widgets.widget-hbox {\n  width: 100% !important;\n  max-width: 100% !important;\n  min-width: 0 !important;\n}\n\n.widget-html-content svg {\n  display: block !important;\n  width: 100% !important;\n  max-width: 100% !important;\n  height: auto !important;\n}\n</style>\n"
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      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "route_nav",
          "title": "Route Guardrails"
        }
      },
      "source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n  <span class=\"ntt-difficulty-pill\">Level 1</span>\n  <div class=\"ntt-cell-row\">\n    <span class=\"ntt-role-pill\">META</span>\n    <span class=\"ntt-kind-pill\">route nav</span>\n  </div>\n  <div class=\"ntt-cell-title\">Route Guardrails</div>\n</div>\n\nYou are at **step 6 of 27** in the only supported route.\n\nNever choose the next notebook manually from the file tree. Use only the links in this cell and the final handoff cell.\n\n**Immediate navigation**\n- Next notebook: [Foundations / 02 Negative Wrapped NTT / Lecture](../02_negative_wrapped_ntt/lecture.ipynb)\n- Previous notebook: [Foundations / 01 Convolution To Toy NTT / Problems](problems.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n\n**Official route chain**\n1. [Start Here](../../START_HERE.ipynb)\n2. [Course Blueprint](../../COURSE_BLUEPRINT.ipynb)\n3. [Foundations / 01 Convolution To Toy NTT / Lecture](lecture.ipynb)\n4. [Foundations / 01 Convolution To Toy NTT / Lab](lab.ipynb)\n5. [Foundations / 01 Convolution To Toy NTT / Problems](problems.ipynb)\n6. **Foundations / 01 Convolution To Toy NTT / Studio** <- you are here\n7. [Foundations / 02 Negative Wrapped NTT / Lecture](../02_negative_wrapped_ntt/lecture.ipynb)\n8. [Foundations / 02 Negative Wrapped NTT / Lab](../02_negative_wrapped_ntt/lab.ipynb)\n9. [Foundations / 02 Negative Wrapped NTT / Problems](../02_negative_wrapped_ntt/problems.ipynb)\n10. [Foundations / 02 Negative Wrapped NTT / Studio](../02_negative_wrapped_ntt/studio.ipynb)\n11. [Butterfly Mechanics / 03 Fast Forward CT / Lecture](../../butterfly_mechanics/03_fast_forward_ct/lecture.ipynb)\n12. [Butterfly Mechanics / 03 Fast Forward CT / Lab](../../butterfly_mechanics/03_fast_forward_ct/lab.ipynb)\n13. [Butterfly Mechanics / 03 Fast Forward CT / Problems](../../butterfly_mechanics/03_fast_forward_ct/problems.ipynb)\n14. [Butterfly Mechanics / 03 Fast Forward CT / Studio](../../butterfly_mechanics/03_fast_forward_ct/studio.ipynb)\n15. [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](../../butterfly_mechanics/04_fast_inverse_gs/lecture.ipynb)\n16. [Butterfly Mechanics / 04 Fast Inverse GS / Lab](../../butterfly_mechanics/04_fast_inverse_gs/lab.ipynb)\n17. [Butterfly Mechanics / 04 Fast Inverse GS / Problems](../../butterfly_mechanics/04_fast_inverse_gs/problems.ipynb)\n18. [Butterfly Mechanics / 04 Fast Inverse GS / Studio](../../butterfly_mechanics/04_fast_inverse_gs/studio.ipynb)\n19. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lecture](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb)\n20. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lab](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb)\n21. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Problems](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb)\n22. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Studio](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb)\n23. [Professional / 06 Debugging NTT Failures / Lecture](../../professional/06_debugging_ntt_failures/lecture.ipynb)\n24. [Professional / 06 Debugging NTT Failures / Lab](../../professional/06_debugging_ntt_failures/lab.ipynb)\n25. [Professional / 06 Debugging NTT Failures / Problems](../../professional/06_debugging_ntt_failures/problems.ipynb)\n26. [Professional / 06 Debugging NTT Failures / Studio](../../professional/06_debugging_ntt_failures/studio.ipynb)\n27. [Course Complete](../../COURSE_COMPLETE.ipynb)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "orientation",
          "title": "Studio Goals"
        }
      },
      "source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n  <span class=\"ntt-difficulty-pill\">Level 1</span>\n  <div class=\"ntt-cell-row\">\n    <span class=\"ntt-role-pill\">META</span>\n    <span class=\"ntt-kind-pill\">orientation</span>\n  </div>\n  <div class=\"ntt-cell-title\">Studio Goals</div>\n</div>\n\nThis studio is about comparison and diagnosis.\nThe learner should leave with a strong visual distinction between cyclic and negacyclic wraparound.\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "explanation",
          "title": "Two Folds, Same Raw Tail, Different Result"
        }
      },
      "source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n  <span class=\"ntt-difficulty-pill\">Level 3</span>\n  <div class=\"ntt-cell-row\">\n    <span class=\"ntt-role-pill\">MANDATORY</span>\n    <span class=\"ntt-kind-pill\">explanation</span>\n  </div>\n  <div class=\"ntt-cell-title\">Two Folds, Same Raw Tail, Different Result</div>\n</div>\n\nIf the raw convolution is fixed, the only thing that changes is the ring rule.\nThat is exactly why the same tail can produce two different reduced polynomials.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "demo",
          "title": "Compare The Two Fold Rules"
        }
      },
      "outputs": [],
      "source": "# MANDATORY\n# title: Compare The Two Fold Rules\n# kind: demo | level: 3\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import schoolbook_convolution\nfrom ntt_learning.visuals import plot_wraparound, wraparound_comparison_player\n\nraw = schoolbook_convolution([1, 2, 3, 4], [5, 6, 7, 8])\nprint(\"raw convolution:\", raw)\ndisplay(wraparound_comparison_player(raw, n=4))\ndisplay(plot_wraparound(raw, n=4, negacyclic=False, title=\"Positive wrap into x^4 - 1\"))\ndisplay(plot_wraparound(raw, n=4, negacyclic=True, title=\"Negative wrap into x^4 + 1\"))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "exercise",
          "title": "Debug Checklist"
        }
      },
      "source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n  <span class=\"ntt-difficulty-pill\">Level 2</span>\n  <div class=\"ntt-cell-row\">\n    <span class=\"ntt-role-pill\">MANDATORY</span>\n    <span class=\"ntt-kind-pill\">exercise</span>\n  </div>\n  <div class=\"ntt-cell-title\">Debug Checklist</div>\n</div>\n\nIf a wraparound result looks wrong, inspect these in order:\n\n1. Was the raw convolution itself correct?\n2. Was the divisor `x^n - 1` or `x^n + 1`?\n3. Did the wrapped tail land in the right slot?\n4. Did the sign flip happen on the wrapped term?\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "exercise",
          "title": "See A Wrong-Sign Failure"
        }
      },
      "outputs": [],
      "source": "# MANDATORY\n# title: See A Wrong-Sign Failure\n# kind: exercise | level: 2\n\nfrom ntt_learning.toy_ntt import schoolbook_convolution, negacyclic_reduce\n\nraw = schoolbook_convolution([1, 2, 3, 4], [5, 6, 7, 8])\nwrong = [raw[0] + raw[4], raw[1] + raw[5], raw[2] + raw[6], raw[3]]\n\nprint(\"raw:\", raw)\nprint(\"wrong sign fold:\", wrong)\nprint(\"correct negacyclic fold:\", negacyclic_reduce(raw, n=4))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "reflection",
          "title": "Reflection"
        }
      },
      "source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n  <span class=\"ntt-difficulty-pill\">Level 2</span>\n  <div class=\"ntt-cell-row\">\n    <span class=\"ntt-role-pill\">MANDATORY</span>\n    <span class=\"ntt-kind-pill\">reflection</span>\n  </div>\n  <div class=\"ntt-cell-title\">Reflection</div>\n</div>\n\nExplain the exact visual difference between \u201cthe wrong-sign fold\u201d and \u201cthe correct negacyclic fold\u201d.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "facultative",
          "difficulty": 4,
          "kind": "exploration",
          "title": "Optional: Fold A Larger Tail"
        }
      },
      "outputs": [],
      "source": "# FACULTATIVE\n# title: Optional: Fold A Larger Tail\n# kind: exploration | level: 4\n\nfrom IPython.display import display\n\nfrom ntt_learning.visuals import plot_wraparound\n\nraw = [4, 8, 12, 16, 9, 5, 1, 7, 11]\ndisplay(plot_wraparound(raw, n=4, negacyclic=True, title=\"Longer tail, same fold rule\"))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "handoff",
          "title": "Next Notebook"
        }
      },
      "source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n  <span class=\"ntt-difficulty-pill\">Level 1</span>\n  <div class=\"ntt-cell-row\">\n    <span class=\"ntt-role-pill\">META</span>\n    <span class=\"ntt-kind-pill\">handoff</span>\n  </div>\n  <div class=\"ntt-cell-title\">Next Notebook</div>\n</div>\n\nYou finished **Foundations / 01 Convolution To Toy NTT / Studio**.\n\n**Primary next action**\n- Next notebook: [Step 7 of 27 - Foundations / 02 Negative Wrapped NTT / Lecture](../02_negative_wrapped_ntt/lecture.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Foundations / 01 Convolution To Toy NTT / Problems](problems.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n"
    }
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        "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb",
        "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb",
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        "notebooks/professional/06_debugging_ntt_failures/lecture.ipynb",
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