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

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "theme",
"title": "Notebook Theme"
}
},
"source": "<style>\n.jp-RenderedHTMLCommon .ntt-cell-head {\n position: relative;\n margin: 0 0 0.8rem 0;\n padding: 0.95rem 1rem 1rem 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-topline {\n display: flex;\n flex-wrap: wrap;\n gap: 0.5rem;\n align-items: center;\n margin-bottom: 0.55rem;\n}\n\n.jp-RenderedHTMLCommon .ntt-kind-pill,\n.jp-RenderedHTMLCommon .ntt-route-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, #fff1b8 0%, #ffd980 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-facultative {\n background: linear-gradient(135deg, #ffe3d4 0%, #ffc3ae 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-kind-pill {\n color: #102a43;\n background: rgba(16,42,67,0.08);\n}\n\n.jp-RenderedHTMLCommon .ntt-route-pill {\n color: #102a43;\n background: rgba(255,255,255,0.82);\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 margin: 0;\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"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "route_nav",
"title": "Route Guardrails"
}
},
"source": "<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-topline\">\n <span class=\"ntt-kind-pill\">route map</span>\n <span class=\"ntt-route-pill\">route help</span>\n </div>\n <h2 class=\"ntt-cell-title\">Route Guardrails</h2>\n</div>\n\nYou are at **step 4 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 / 01 Convolution To Toy NTT / Problems](problems.ipynb)\n- Previous notebook: [Foundations / 01 Convolution To Toy NTT / Lecture](lecture.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** <- you are here\n5. [Foundations / 01 Convolution To Toy NTT / Problems](problems.ipynb)\n6. [Foundations / 01 Convolution To Toy NTT / Studio](studio.ipynb)\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": "Lab Goals"
}
},
"source": "<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-topline\">\n <span class=\"ntt-kind-pill\">big picture</span>\n <span class=\"ntt-route-pill\">route help</span>\n </div>\n <h2 class=\"ntt-cell-title\">Lab Goals</h2>\n</div>\n\nPredict the movement before you run the code.\n\nThe point is not just to see the picture after the fact.\nThe point is to force your eye to anticipate where the products and wraparound terms will land.\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "exercise",
"title": "Exercise 1"
}
},
"source": "<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 2</span>\n <div class=\"ntt-cell-topline\">\n <span class=\"ntt-kind-pill\">exercise</span>\n <span class=\"ntt-route-pill\">core path</span>\n </div>\n <h2 class=\"ntt-cell-title\">Exercise 1</h2>\n</div>\n\nBefore running the next cell:\n\n- name the diagonal sums of the raw schoolbook grid\n- say which tail terms will wrap into slot `0`\n- say whether they add or subtract in `x^4 + 1`\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "exercise",
"title": "Run The Prediction Check"
}
},
"outputs": [],
"source": "# Run The Prediction Check\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import negacyclic_multiply, schoolbook_convolution\nfrom ntt_learning.visuals import plot_convolution_grid, plot_wraparound, schoolbook_diagonal_player, wraparound_comparison_player\n\nleft = [3, 0, 2, 1]\nright = [1, 4, 0, 2]\nraw = schoolbook_convolution(left, right)\n\nprint(\"raw convolution:\", raw)\nprint(\"negacyclic result:\", negacyclic_multiply(left, right, n=4))\ndisplay(schoolbook_diagonal_player(left, right))\ndisplay(wraparound_comparison_player(raw, n=4))\ndisplay(plot_convolution_grid(left, right, title=\"Prediction check grid\"))\ndisplay(plot_wraparound(raw, n=4, negacyclic=True, title=\"Prediction check fold\"))\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "exercise",
"title": "Exercise 2"
}
},
"source": "<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 2</span>\n <div class=\"ntt-cell-topline\">\n <span class=\"ntt-kind-pill\">exercise</span>\n <span class=\"ntt-route-pill\">core path</span>\n </div>\n <h2 class=\"ntt-cell-title\">Exercise 2</h2>\n</div>\n\nPick one number in the raw tail and follow it all the way to its final slot.\nDo not say \u201cit wraps around\u201d.\nSay exactly:\n\n- where it started\n- how many wraps happened\n- whether the sign flipped\n- where it finished\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "exercise",
"title": "A Second Visual Drill"
}
},
"outputs": [],
"source": "# A Second Visual Drill\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([2, 5, 0, 1], [1, 0, 3, 2])\nprint(\"raw convolution:\", raw)\ndisplay(wraparound_comparison_player(raw, n=4))\ndisplay(plot_wraparound(raw, n=4, negacyclic=True, title=\"Trace one tail coefficient by eye\"))\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "reflection",
"title": "Reflection"
}
},
"source": "<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 2</span>\n <div class=\"ntt-cell-topline\">\n <span class=\"ntt-kind-pill\">reflection</span>\n <span class=\"ntt-route-pill\">core path</span>\n </div>\n <h2 class=\"ntt-cell-title\">Reflection</h2>\n</div>\n\nReflection prompt:\n\n- What felt easier to see in the grid than in symbolic polynomial notation?\n- What exactly makes negacyclic folding more annoying than ordinary wraparound?\n- If you had to explain `x^n + 1` to somebody visually, what would you draw?\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "facultative",
"difficulty": 4,
"kind": "exploration",
"title": "Optional: Try Your Own Arrays"
}
},
"outputs": [],
"source": "# Optional: Try Your Own Arrays\n\nimport ipywidgets as widgets\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import schoolbook_convolution\nfrom ntt_learning.visuals import plot_convolution_grid, plot_wraparound\n\ndef preview(a0=1, a1=2, a2=3, a3=4, b0=5, b1=6, b2=7, b3=8):\n left = [a0, a1, a2, a3]\n right = [b0, b1, b2, b3]\n raw = schoolbook_convolution(left, right)\n display(plot_convolution_grid(left, right, title=\"Interactive schoolbook grid\"))\n display(plot_wraparound(raw, n=4, negacyclic=True, title=\"Interactive negacyclic fold\"))\n\ndisplay(\n widgets.interact(\n preview,\n a0=(0, 6),\n a1=(0, 6),\n a2=(0, 6),\n a3=(0, 6),\n b0=(0, 6),\n b1=(0, 6),\n b2=(0, 6),\n b3=(0, 6),\n )\n)\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "handoff",
"title": "Next Notebook"
}
},
"source": "<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-topline\">\n <span class=\"ntt-kind-pill\">next step</span>\n <span class=\"ntt-route-pill\">route help</span>\n </div>\n <h2 class=\"ntt-cell-title\">Next Notebook</h2>\n</div>\n\nYou finished **Foundations / 01 Convolution To Toy NTT / Lab**.\n\n**Primary next action**\n- Next notebook: [Step 5 of 27 - Foundations / 01 Convolution To Toy NTT / Problems](problems.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Foundations / 01 Convolution To Toy NTT / Lecture](lecture.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n"
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"name": "python"
},
"ntt_learning": {
"title": "Lab: Convolution To Toy NTT",
"contract_version": "0.2",
"sequence": [
"notebooks/START_HERE.ipynb",
"notebooks/COURSE_BLUEPRINT.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/lecture.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/lab.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/problems.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/studio.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/lecture.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/lab.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/problems.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/studio.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/lecture.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/lab.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/problems.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/studio.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/lecture.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/lab.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/problems.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/studio.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb",
"notebooks/professional/06_debugging_ntt_failures/lecture.ipynb",
"notebooks/professional/06_debugging_ntt_failures/lab.ipynb",
"notebooks/professional/06_debugging_ntt_failures/problems.ipynb",
"notebooks/professional/06_debugging_ntt_failures/studio.ipynb",
"notebooks/COURSE_COMPLETE.ipynb"
]
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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