diff --git a/TODO.md b/TODO.md
index df99342..1dc286d 100644
--- a/TODO.md
+++ b/TODO.md
@@ -1,6 +1,7 @@
 # system-a
 
-[system-a] `gradientDescentRms`
+[system-a] `gradientDescentAdam`
+[system-a] test `gradientDescentAdam` by `plane`
 
 # the-book
 
diff --git a/src/system-a/gradient-descent/gradientDescentRms.ts b/src/system-a/gradient-descent/gradientDescentRms.ts
index 416bc45..f7a26f6 100644
--- a/src/system-a/gradient-descent/gradientDescentRms.ts
+++ b/src/system-a/gradient-descent/gradientDescentRms.ts
@@ -6,7 +6,9 @@ import { smooth } from "./smooth.js"
 
 const stabilizer = 1e-8
 
-export function gradientDescentRms(options: {
+// NOTE RMS stands for root mean square.
+
+export function rmsRepresentation(options: {
   learningRate: number
   decayRate: number
 }): Representation<[Tensor, Tensor]> {
@@ -26,9 +28,9 @@ export function gradientDescentRms(options: {
   }
 }
 
-export function gradientDescentVelocity(options: {
+export function gradientDescentRms(options: {
   learningRate: number
   decayRate: number
 }) {
-  return gradientDescent(gradientDescentRms(options))
+  return gradientDescent(rmsRepresentation(options))
 }
diff --git a/src/system-a/targets/plane.test.ts b/src/system-a/targets/plane.test.ts
index 21f1b9f..e013ab7 100644
--- a/src/system-a/targets/plane.test.ts
+++ b/src/system-a/targets/plane.test.ts
@@ -2,6 +2,7 @@ import assert from "node:assert"
 import { test } from "node:test"
 import { gradientDescentLonely } from "../gradient-descent/gradientDescentLonely.js"
 import { gradientDescentNaked } from "../gradient-descent/gradientDescentNaked.js"
+import { gradientDescentRms } from "../gradient-descent/gradientDescentRms.js"
 import { gradientDescentVelocity } from "../gradient-descent/gradientDescentVelocity.js"
 import type { GradientDescentFn } from "../gradient-descent/index.js"
 import { l2Loss } from "../loss.js"
@@ -25,7 +26,7 @@ test("plane -- extended", () => {
   )
 })
 
-function testGradientDescentByLine(
+function testGradientDescentByPlane(
   gradientDescentFn: GradientDescentFn,
   options: {
     revs: number
@@ -53,20 +54,27 @@ function testGradientDescentByLine(
 }
 
 test("plane -- gradientDescentNaked", () => {
-  testGradientDescentByLine(gradientDescentNaked({ learningRate: 0.001 }), {
+  testGradientDescentByPlane(gradientDescentNaked({ learningRate: 0.001 }), {
     revs: 15000,
   })
 })
 
 test("plane -- gradientDescentLonely", () => {
-  testGradientDescentByLine(gradientDescentLonely({ learningRate: 0.001 }), {
+  testGradientDescentByPlane(gradientDescentLonely({ learningRate: 0.001 }), {
     revs: 15000,
   })
 })
 
 test("plane -- gradientDescentVelocity", () => {
-  testGradientDescentByLine(
+  testGradientDescentByPlane(
     gradientDescentVelocity({ learningRate: 0.001, relayFactor: 0.9 }),
     { revs: 5000 },
   )
 })
+
+test("plane -- gradientDescentRms", () => {
+  testGradientDescentByPlane(
+    gradientDescentRms({ learningRate: 0.01, decayRate: 0.9 }),
+    { revs: 3000 },
+  )
+})