{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "orientation",
          "title": "Lab Goals"
        }
      },
      "source": "## META | difficulty 1 | Lab Goals\n\nPredict the BO input and the final scaling before you run the stage explorer.\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "route_nav",
          "title": "Route Guardrails"
        }
      },
      "source": "## META | difficulty 1 | Route Guardrails\n\nYou are at **step 16 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: [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n- Previous notebook: [Butterfly Mechanics / 04 Fast Inverse GS / 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](../../foundations/01_convolution_to_toy_ntt/lecture.ipynb)\n4. [Foundations / 01 Convolution To Toy NTT / Lab](../../foundations/01_convolution_to_toy_ntt/lab.ipynb)\n5. [Foundations / 01 Convolution To Toy NTT / Problems](../../foundations/01_convolution_to_toy_ntt/problems.ipynb)\n6. [Foundations / 01 Convolution To Toy NTT / Studio](../../foundations/01_convolution_to_toy_ntt/studio.ipynb)\n7. [Foundations / 02 Negative Wrapped NTT / Lecture](../../foundations/02_negative_wrapped_ntt/lecture.ipynb)\n8. [Foundations / 02 Negative Wrapped NTT / Lab](../../foundations/02_negative_wrapped_ntt/lab.ipynb)\n9. [Foundations / 02 Negative Wrapped NTT / Problems](../../foundations/02_negative_wrapped_ntt/problems.ipynb)\n10. [Foundations / 02 Negative Wrapped NTT / Studio](../../foundations/02_negative_wrapped_ntt/studio.ipynb)\n11. [Butterfly Mechanics / 03 Fast Forward CT / Lecture](../03_fast_forward_ct/lecture.ipynb)\n12. [Butterfly Mechanics / 03 Fast Forward CT / Lab](../03_fast_forward_ct/lab.ipynb)\n13. [Butterfly Mechanics / 03 Fast Forward CT / Problems](../03_fast_forward_ct/problems.ipynb)\n14. [Butterfly Mechanics / 03 Fast Forward CT / Studio](../03_fast_forward_ct/studio.ipynb)\n15. [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](lecture.ipynb)\n16. **Butterfly Mechanics / 04 Fast Inverse GS / Lab** <- you are here\n17. [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n18. [Butterfly Mechanics / 04 Fast Inverse GS / Studio](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": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Exercise 1"
        }
      },
      "source": "## MANDATORY | difficulty 3 | Exercise 1\n\nExplain before running the next cell:\n\n- why the GS input must be BO in the standard schedule\n- why the unscaled output is not yet the original signal\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Prediction Check"
        }
      },
      "outputs": [],
      "source": "# MANDATORY | difficulty 3 | Prediction Check\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_intt_psi_gs_trace\nfrom ntt_learning.visuals import interactive_trace\n\ntrace = fast_intt_psi_gs_trace([1467, 3471, 2807, 7621], 7681, 1925)\ndisplay(interactive_trace(trace, title=\"Check your GS prediction\"))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Exercise 2"
        }
      },
      "source": "## MANDATORY | difficulty 3 | Exercise 2\n\nPredict the bit-reversal of `[0,1,2,3,4,5,6,7]` before running the next cell.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Prediction Check For Ordering"
        }
      },
      "outputs": [],
      "source": "# MANDATORY | difficulty 3 | Prediction Check For Ordering\n\nfrom ntt_learning.toy_ntt import bit_reversed_order\n\nprint(bit_reversed_order([0, 1, 2, 3, 4, 5, 6, 7]))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "reflection",
          "title": "Reflection"
        }
      },
      "source": "## MANDATORY | difficulty 2 | Reflection\n\nReflection prompt:\n\n- Which part of GS felt like a true inverse to you?\n- Which part felt like pure bookkeeping?\n- Why is the ordering story impossible to ignore?\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "facultative",
          "difficulty": 4,
          "kind": "exploration",
          "title": "Optional: Explore Another BO Input"
        }
      },
      "outputs": [],
      "source": "# FACULTATIVE | difficulty 4 | Optional: Explore Another BO Input\n\nimport ipywidgets as widgets\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_intt_psi_gs_trace\nfrom ntt_learning.visuals import interactive_trace\n\ndef preview(x0=1467, x1=3471, x2=2807, x3=7621):\n    trace = fast_intt_psi_gs_trace([x0, x1, x2, x3], 7681, 1925)\n    display(interactive_trace(trace, title=\"Interactive GS trace\"))\n\ndisplay(\n    widgets.interact(\n        preview,\n        x0=(0, 7680),\n        x1=(0, 7680),\n        x2=(0, 7680),\n        x3=(0, 7680),\n    )\n)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "handoff",
          "title": "Next Notebook"
        }
      },
      "source": "## META | difficulty 1 | Next Notebook\n\nYou finished **Butterfly Mechanics / 04 Fast Inverse GS / Lab**.\n\n**Primary next action**\n- Next notebook: [Step 17 of 27 - Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Butterfly Mechanics / 04 Fast Inverse GS / 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: Fast Inverse GS",
      "contract_version": "0.2",
      "sequence": [
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        "notebooks/COURSE_BLUEPRINT.ipynb",
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        "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",
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        "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"
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}