1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
|
<?php return [
'version' => '1.0',
'info' => [
'style' => 'ROA',
'product' => 'EduTutor',
'version' => '2025-07-07',
],
'directories' => [
'CutQuestions',
'AnswerSSE',
],
'components' => [
'schemas' => [],
],
'apis' => [
'CutQuestions' => [
'summary' => '切题及题目结构化接口,客户输入试卷或整页题目图片,算法返回每个题目的位置信息以及结构化(题干、选项、答案等)信息。',
'path' => '/service/cutApi',
'methods' => [
'post',
],
'schemes' => [
'https',
],
'security' => [
[
'AK' => [],
],
],
'consumes' => [
'application/json',
],
'produces' => [
'application/json',
],
'operationType' => 'readAndWrite',
'deprecated' => false,
'systemTags' => [
'operationType' => 'none',
'riskType' => 'none',
'chargeType' => 'paid',
'tenantRelevance' => 'publicInformation',
],
'parameters' => [
[
'name' => 'workspaceId',
'in' => 'query',
'schema' => [
'description' => '当前请求所使用的百炼业务空间 id。',
'type' => 'string',
'required' => true,
'example' => 'llm-1ijrzuv3v0ivvls7',
],
],
[
'name' => 'body',
'in' => 'body',
'style' => 'json',
'schema' => [
'description' => '请求body。',
'type' => 'object',
'properties' => [
'image' => [
'description' => '试卷、题目图片链接。',
'type' => 'string',
'required' => true,
'example' => 'https://oss.xxx.com/xx.png',
],
'parameters' => [
'description' => '参数配置。',
'type' => 'object',
'properties' => [
'struct' => [
'description' => '是否返回结构化信息。',
'type' => 'boolean',
'required' => true,
'example' => 'true',
],
'extract_images' => [
'description' => '是否返回子题临时oss链接,便于后续答题直接使用。',
'type' => 'boolean',
'required' => true,
'example' => 'true',
],
],
'required' => true,
],
],
'required' => false,
],
],
],
'responses' => [
200 => [
'schema' => [
'title' => 'Schema of Response',
'description' => 'Schema of Response',
'type' => 'object',
'properties' => [
'requestId' => [
'description' => '请求id,每次请求都是唯一值,便于后续排查问题。',
'type' => 'string',
'example' => '1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB',
],
'success' => [
'description' => '调用是否成功。',
'type' => 'boolean',
'example' => 'True',
],
'code' => [
'description' => '响应状态码。',
'type' => 'string',
'example' => 'SUCCESS',
],
'httpStatusCode' => [
'description' => 'http状态码。',
'type' => 'integer',
'format' => 'int32',
'example' => '200',
],
'message' => [
'description' => '返回码描述。',
'type' => 'string',
'example' => 'success',
],
'data' => [
'description' => '算法返回结果。',
'type' => 'string',
'example' => '\'{'."\n"
.' "questions": ['."\n"
.' {'."\n"
.' "pos_list": ['."\n"
.' ['."\n"
.' 21,'."\n"
.' 0,'."\n"
.' 364,'."\n"
.' 0,'."\n"
.' 364,'."\n"
.' 82,'."\n"
.' 21,'."\n"
.' 82'."\n"
.' ]'."\n"
.' ],'."\n"
.' "sub_images": ['."\n"
.' "http://duguang-mld.oss-accelerate.aliyuncs.com/ocr_edu/1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB_0_0.png?OSSAccessKeyId=LTAI5tPtEwpyT4JR9Gym****&Expires=1755593474&Signature=SnqwepQVvZ51PnUGtpH0fWV50JI%3D"'."\n"
.' ],'."\n"
.' "merged_image": "http://duguang-mld.oss-accelerate.aliyuncs.com/ocr_edu/1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB_0_0.png?OSSAccessKeyId=LTAI5tPtEwpyT4JR9Gy****&Expires=1755593474&Signature=SnqwepQVvZ51PnUGtpH0fWV50JI%3D",'."\n"
.' "info": {'."\n"
.' "stem": {'."\n"
.' "text": "8. 若 \\\\\\\\(a + b = -1\\\\\\\\), \\\\\\\\(ab = 4\\\\\\\\), 则 \\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\) 的值为 _ 。",'."\n"
.' "pos_list": ['."\n"
.' ['."\n"
.' 21,'."\n"
.' 4,'."\n"
.' 364,'."\n"
.' 4,'."\n"
.' 364,'."\n"
.' 78,'."\n"
.' 21,'."\n"
.' 78'."\n"
.' ]'."\n"
.' ]'."\n"
.' },'."\n"
.' "option": [],'."\n"
.' "figure": [],'."\n"
.' "answer": ['."\n"
.' {'."\n"
.' "text": "-17",'."\n"
.' "pos_list": ['."\n"
.' ['."\n"
.' 225,'."\n"
.' 51,'."\n"
.' 262,'."\n"
.' 51,'."\n"
.' 262,'."\n"
.' 70,'."\n"
.' 225,'."\n"
.' 70'."\n"
.' ]'."\n"
.' ]'."\n"
.' }'."\n"
.' ],'."\n"
.' "type": "填空题",'."\n"
.' "subquestion": []'."\n"
.' }'."\n"
.' }'."\n"
.' ]'."\n"
.'}\'',
],
'input_tokens' => [
'description' => '此次调用输入消耗的token数。',
'type' => 'integer',
'format' => 'int32',
'example' => '80',
],
'output_tokens' => [
'description' => '此次调用输出消耗的token数。',
'type' => 'integer',
'format' => 'int32',
'example' => '38',
],
],
],
],
],
'staticInfo' => [
'returnType' => 'synchronous',
],
'responseDemo' => '[{"errorExample":"","example":"{\\n \\"requestId\\": \\"1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB\\",\\n \\"success\\": true,\\n \\"code\\": \\"SUCCESS\\",\\n \\"httpStatusCode\\": 200,\\n \\"message\\": \\"success\\",\\n \\"data\\": \\"\'{\\\\n \\\\\\"questions\\\\\\": [\\\\n {\\\\n \\\\\\"pos_list\\\\\\": [\\\\n [\\\\n 21,\\\\n 0,\\\\n 364,\\\\n 0,\\\\n 364,\\\\n 82,\\\\n 21,\\\\n 82\\\\n ]\\\\n ],\\\\n \\\\\\"sub_images\\\\\\": [\\\\n \\\\\\"http://duguang-mld.oss-accelerate.aliyuncs.com/ocr_edu/1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB_0_0.png?OSSAccessKeyId=LTAI5tPtEwpyT4JR9Gym****&Expires=1755593474&Signature=SnqwepQVvZ51PnUGtpH0fWV50JI%3D\\\\\\"\\\\n ],\\\\n \\\\\\"merged_image\\\\\\": \\\\\\"http://duguang-mld.oss-accelerate.aliyuncs.com/ocr_edu/1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB_0_0.png?OSSAccessKeyId=LTAI5tPtEwpyT4JR9Gy****&Expires=1755593474&Signature=SnqwepQVvZ51PnUGtpH0fWV50JI%3D\\\\\\",\\\\n \\\\\\"info\\\\\\": {\\\\n \\\\\\"stem\\\\\\": {\\\\n \\\\\\"text\\\\\\": \\\\\\"8. 若 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(a + b = -1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\), \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(ab = 4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\), 则 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 的值为 _ 。\\\\\\",\\\\n \\\\\\"pos_list\\\\\\": [\\\\n [\\\\n 21,\\\\n 4,\\\\n 364,\\\\n 4,\\\\n 364,\\\\n 78,\\\\n 21,\\\\n 78\\\\n ]\\\\n ]\\\\n },\\\\n \\\\\\"option\\\\\\": [],\\\\n \\\\\\"figure\\\\\\": [],\\\\n \\\\\\"answer\\\\\\": [\\\\n {\\\\n \\\\\\"text\\\\\\": \\\\\\"-17\\\\\\",\\\\n \\\\\\"pos_list\\\\\\": [\\\\n [\\\\n 225,\\\\n 51,\\\\n 262,\\\\n 51,\\\\n 262,\\\\n 70,\\\\n 225,\\\\n 70\\\\n ]\\\\n ]\\\\n }\\\\n ],\\\\n \\\\\\"type\\\\\\": \\\\\\"填空题\\\\\\",\\\\n \\\\\\"subquestion\\\\\\": []\\\\n }\\\\n }\\\\n ]\\\\n}\'\\",\\n \\"input_tokens\\": 80,\\n \\"output_tokens\\": 38\\n}","type":"json"}]',
'title' => '试卷切题',
'description' => '开通 EduTutor 服务。本接口在公测阶段,每个账号每天可以免费调用1000次。',
'responseParamsDescription' => '#### 算法结果字段 data '."\n"
.'+ 需要序列化,字段说明如下:'."\n"
."\n"
.'|字段|类型|描述|示例值|'."\n"
.'|-----|---|--|--|'."\n"
.'questions | array | 模型切出来的题目数组。| '."\n"
.'questions[i].pos_list | array | 第i道题目的坐标框(可能含有多个)。 | [[21,0,364,0,364,82,21,82]] | '."\n"
.'questions[i].sub_images | array | 根据坐标框提取出来的子图图片链接(7天有效)。| |'."\n"
.'questions[i].merged_image | string | 所有子图合并之后的题目完整图片链接(7天有效)。| |'."\n"
.'questions[i].info | object | 题目结构化信息。| |'."\n"
.'questions[i].info.type | string | 题目类型:选择题/填空题/判断题/问答题/作文题/其他。 | 填空题 |'."\n"
.'questions[i].info.stem | array |题干信息。| | '."\n"
.'questions[i].info.stem.text | string | 题干文本信息。| | '."\n"
.'questions[i].info.stem.pos_list | array | 题干坐标框信息。| |'."\n"
.'questions[i].info.option | array | 选项信息。| | '."\n"
.'questions[i].info.option[j].text | string | 选项文本信息。| |'."\n"
.'questions[i].info.option[j].pos_list | array | 选项位置信息。 | | '."\n"
.'questions[i].info.figure | array | 插图信息。| |'."\n"
.'questions[i].info.figure[k].pos_list | array | 插图位置信息。| |'."\n"
.'questions[i].info.answer | array | 答案信息。 | |'."\n"
.'questions[i].info.answer[m].pos_list | array | 答案位置信息。| "-17" |'."\n"
.'questions[i].info.answer[m].text | string | 答案文本信息。| | '."\n"
.'questions[i].info.subquestion | array | 子题信息(结构和info一致)。| |'."\n"
."\n"
.'举例:'."\n"
.'```'."\n"
.'{'."\n"
.' "questions": ['."\n"
.' {'."\n"
.' "pos_list": ['."\n"
.' ['."\n"
.' 21,'."\n"
.' 0,'."\n"
.' 364,'."\n"
.' 0,'."\n"
.' 364,'."\n"
.' 82,'."\n"
.' 21,'."\n"
.' 82'."\n"
.' ]'."\n"
.' ],'."\n"
.' "sub_images": ['."\n"
.' "http://xxxxx/sub_images/1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB_0_0.png"'."\n"
.' ],'."\n"
.' "merged_image": "http://xxxxx/sub_images/1CE2851D-96D6-51D0-8ADA-EB7ACAF374BB.png",'."\n"
.' "info": {'."\n"
.' "stem": {'."\n"
.' "text": "8. 若 \\\\\\\\(a + b = -1\\\\\\\\), \\\\\\\\(ab = 4\\\\\\\\), 则 \\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\) 的值为 _ 。",'."\n"
.' "pos_list": ['."\n"
.' ['."\n"
.' 21,'."\n"
.' 4,'."\n"
.' 364,'."\n"
.' 4,'."\n"
.' 364,'."\n"
.' 78,'."\n"
.' 21,'."\n"
.' 78'."\n"
.' ]'."\n"
.' ]'."\n"
.' },'."\n"
.' "option": [],'."\n"
.' "figure": [],'."\n"
.' "answer": ['."\n"
.' {'."\n"
.' "text": "-17",'."\n"
.' "pos_list": ['."\n"
.' ['."\n"
.' 225,'."\n"
.' 51,'."\n"
.' 262,'."\n"
.' 51,'."\n"
.' 262,'."\n"
.' 70,'."\n"
.' 225,'."\n"
.' 70'."\n"
.' ]'."\n"
.' ]'."\n"
.' }'."\n"
.' ],'."\n"
.' "type": "填空题",'."\n"
.' "subquestion": []'."\n"
.' }'."\n"
.' }'."\n"
.' ]'."\n"
.'}'."\n"
.'```',
],
'AnswerSSE' => [
'summary' => '流式答题解析接口,客户输入需要解答题题目文本或图片,算法会返回题目详细的解答内容。',
'path' => '/service/answerSSE',
'methods' => [
'post',
],
'schemes' => [
'https',
'sse',
],
'security' => [
[
'AK' => [],
],
],
'consumes' => [
'application/json',
],
'produces' => [
'application/octet-stream',
],
'operationType' => 'readAndWrite',
'deprecated' => false,
'systemTags' => [
'operationType' => 'none',
'riskType' => 'none',
'chargeType' => 'paid',
'tenantRelevance' => 'publicInformation',
],
'parameters' => [
[
'name' => 'workspaceId',
'in' => 'query',
'schema' => [
'description' => '当前请求所使用的百炼业务空间 id。',
'type' => 'string',
'required' => true,
'example' => 'llm-1ijrzuv3v0ivvls7',
],
],
[
'name' => 'body',
'in' => 'body',
'style' => 'json',
'schema' => [
'description' => '请求body。',
'type' => 'object',
'properties' => [
'messages' => [
'description' => '多轮对话内容。',
'type' => 'array',
'items' => [
'type' => 'object',
'properties' => [
'role' => [
'description' => '当前对话的角色。',
'type' => 'string',
'required' => true,
'example' => 'user',
'enum' => [
'user',
'assistant',
],
],
'content' => [
'description' => '当前对话内容。',
'type' => 'array',
'items' => [
'description' => '对话内容,可以是文本(text)、图片(image)。',
'type' => 'object',
'required' => false,
'additionalProperties' => [
'type' => 'string',
'example' => '{"image": "image-url"}'."\n"
.'{"text": "回答这个问题"}',
'description' => '文本或图片链接。',
],
],
'required' => false,
],
],
'required' => false,
],
'required' => false,
],
'parameters' => [
'description' => '参数配置。',
'type' => 'object',
'properties' => [
'grade' => [
'description' => '年级,输入为整型数字,可选如下:'."\n"
.'0--学前、'."\n"
.'1--一年级、'."\n"
.'2--二年级、'."\n"
.'3--三年级、'."\n"
.'4--四年级、'."\n"
.'5--五年级、'."\n"
.'6--六年级、'."\n"
.'7--七年级(初一)、'."\n"
.'8--八年级(初二)、'."\n"
.'9--九年级(初三)、'."\n"
.'10--高一、'."\n"
.'11--高二、'."\n"
.'12--高三、'."\n"
.'14--大学一年级、'."\n"
.'15--大学二年级、'."\n"
.'16--大学三年级、'."\n"
.'17--大学四年级、'."\n"
.'99--其他。',
'type' => 'integer',
'format' => 'int32',
'required' => false,
'example' => '6',
'default' => '0',
],
'stage' => [
'description' => '学段。',
'type' => 'string',
'required' => false,
'example' => 'other',
'default' => 'other',
'enum' => [
'other',
'pre',
'elementary',
'middle',
'high',
'higher',
],
],
'subject' => [
'description' => '学科名称。',
'type' => 'string',
'required' => false,
'example' => 'other',
'default' => 'other',
'enum' => [
'other',
'math',
'chinese',
'english',
'physics',
'chemistry',
'biology',
'history',
'geography',
'politics',
'program',
],
],
],
'required' => false,
],
],
'required' => false,
],
],
],
'responses' => [
200 => [
'schema' => [
'title' => 'Schema of Response',
'description' => 'Schema of Response',
'type' => 'object',
'properties' => [
'requestId' => [
'description' => '请求id,每次请求都是唯一值,便于后续排查问题。',
'type' => 'string',
'example' => 'CED92479-FFA7-5B8F-AE6F-C8693BB4941C',
],
'success' => [
'description' => '调用是否成功。',
'type' => 'boolean',
'example' => 'True',
],
'code' => [
'description' => '响应状态码。',
'type' => 'string',
'example' => 'SUCCESS',
],
'httpStatusCode' => [
'description' => 'http状态码。',
'type' => 'integer',
'format' => 'int32',
'example' => '200',
],
'message' => [
'description' => '返回码描述。',
'type' => 'string',
'example' => 'success',
],
'data' => [
'description' => '返回结果。',
'type' => 'string',
'example' => '\'{"message": {"content": [{"text": "### 【考点分析】:\\\\n本题涉及的核心知识点包括代数表达式的简化和代值计算。题目给出了 \\\\\\\\(a + b = -1\\\\\\\\) 和 \\\\\\\\(ab = 4\\\\\\\\) 两个条件,要求我们求解表达式 \\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\) 的值。这类题目常见于代数基础部分,考查学生对代数式的基本运算和代入法的掌握。\\\\n\\\\n### 【方法点拨】:\\\\n1. **简化表达式**:首先对给定的表达式进行简化,合并同类项。\\\\n2. **代入已知条件**:将 \\\\\\\\(a + b = -1\\\\\\\\) 和 \\\\\\\\(ab = 4\\\\\\\\) 代入简化后的表达式中,进行计算。\\\\n3. **逐步求解**:通过逐步代入和计算,得到最终结果。\\\\n\\\\n### 【详细解析】:\\\\n\\\\n#### 第一步:简化表达式\\\\n表达式为 \\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\)。\\\\n\\\\n先去掉括号并合并同类项:\\\\n\\\\\\\\[\\\\n(4a - 5b - 3ab) - (3a - 6b + ab) = 4a - 5b - 3ab - 3a + 6b - ab\\\\n\\\\\\\\]\\\\n\\\\n合并同类项:\\\\n\\\\\\\\[\\\\n= (4a - 3a) + (-5b + 6b) + (-3ab - ab) = a + b - 4ab\\\\n\\\\\\\\]\\\\n\\\\n#### 第二步:代入已知条件\\\\n根据题目条件 \\\\\\\\(a + b = -1\\\\\\\\) 和 \\\\\\\\(ab = 4\\\\\\\\),将这些值代入简化后的表达式:\\\\n\\\\\\\\[\\\\na + b - 4ab = -1 - 4 \\\\\\\\times 4 = -1 - 16 = -17\\\\n\\\\\\\\]\\\\n\\\\n#### 第三步:得出最终结果\\\\n因此,表达式的值为 \\\\\\\\(-17\\\\\\\\)。\\\\n\\\\n### 【最终答案】:\\\\n\\\\\\\\(\\\\\\\\boxed{-17}\\\\\\\\) \\\\n\\\\n所以,该表达式的值为 \\\\\\\\(\\\\\\\\boxed{-17}\\\\\\\\)。"}], "role": "assistant"}}\'',
],
'finish_reason' => [
'description' => '流式输出标志位,用于判断流式输出是否结果,结束时返回stop。',
'type' => 'string',
'example' => 'stop',
],
'input_tokens' => [
'description' => '此次调用输入消耗的token数。',
'type' => 'integer',
'format' => 'int32',
'example' => '654',
],
'output_tokens' => [
'description' => '此次调用输出消耗的token数。',
'type' => 'integer',
'format' => 'int32',
'example' => '457',
],
],
],
],
],
'staticInfo' => [
'returnType' => 'synchronous',
],
'responseDemo' => '[{"errorExample":"","example":"{\\n \\"requestId\\": \\"CED92479-FFA7-5B8F-AE6F-C8693BB4941C\\",\\n \\"success\\": true,\\n \\"code\\": \\"SUCCESS\\",\\n \\"httpStatusCode\\": 200,\\n \\"message\\": \\"success\\",\\n \\"data\\": \\"\'{\\\\\\"message\\\\\\": {\\\\\\"content\\\\\\": [{\\\\\\"text\\\\\\": \\\\\\"### 【考点分析】:\\\\\\\\\\\\\\\\n本题涉及的核心知识点包括代数表达式的简化和代值计算。题目给出了 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(a + b = -1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 和 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(ab = 4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 两个条件,要求我们求解表达式 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 的值。这类题目常见于代数基础部分,考查学生对代数式的基本运算和代入法的掌握。\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n### 【方法点拨】:\\\\\\\\\\\\\\\\n1. **简化表达式**:首先对给定的表达式进行简化,合并同类项。\\\\\\\\\\\\\\\\n2. **代入已知条件**:将 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(a + b = -1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 和 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(ab = 4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 代入简化后的表达式中,进行计算。\\\\\\\\\\\\\\\\n3. **逐步求解**:通过逐步代入和计算,得到最终结果。\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n### 【详细解析】:\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n#### 第一步:简化表达式\\\\\\\\\\\\\\\\n表达式为 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\)。\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n先去掉括号并合并同类项:\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\[\\\\\\\\\\\\\\\\n(4a - 5b - 3ab) - (3a - 6b + ab) = 4a - 5b - 3ab - 3a + 6b - ab\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\]\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n合并同类项:\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\[\\\\\\\\\\\\\\\\n= (4a - 3a) + (-5b + 6b) + (-3ab - ab) = a + b - 4ab\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\]\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n#### 第二步:代入已知条件\\\\\\\\\\\\\\\\n根据题目条件 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(a + b = -1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) 和 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(ab = 4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\),将这些值代入简化后的表达式:\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\[\\\\\\\\\\\\\\\\na + b - 4ab = -1 - 4 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\times 4 = -1 - 16 = -17\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\]\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n#### 第三步:得出最终结果\\\\\\\\\\\\\\\\n因此,表达式的值为 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(-17\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\)。\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n### 【最终答案】:\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\boxed{-17}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) \\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\n所以,该表达式的值为 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\boxed{-17}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\)。\\\\\\"}], \\\\\\"role\\\\\\": \\\\\\"assistant\\\\\\"}}\'\\",\\n \\"finish_reason\\": \\"stop\\",\\n \\"input_tokens\\": 654,\\n \\"output_tokens\\": 457\\n}","type":"json"}]',
'title' => '解题辅导',
'description' => '开通 EduTutor 服务。本接口在公测阶段,每个账号每天可以免费调用1000次。',
'responseParamsDescription' => '### 算法结果字段 data'."\n"
.'+ 需要序列化,字段说明如下:'."\n"
."\n"
.'| 名称 | 类型 | 描述 | 示例值 |'."\n"
.'|-----|------|-----|-------|'."\n"
.'| message | array | | |'."\n"
.'| message[0].content | array | | |'."\n"
.'| message[0].content[0].text | string | 大模型解题结果。 | "### 【考点分析】:\\\\n本题涉及的核心知识点包括代数表..." |'."\n"
.'| message[0].role | string | 角色。 | "assistant" |'."\n"
."\n"
.'举例如下:'."\n"
.'```'."\n"
.'{'."\n"
.' "message": {'."\n"
.' "content": ['."\n"
.' {'."\n"
.' "text": "### 【考点分析】:\\\\n本题涉及的核心知识点包括代数表达式的简化和代值计算。题目给出了 \\\\\\\\(a + b = -1\\\\\\\\) 和 \\\\\\\\(ab = 4\\\\\\\\) 两个条件,要求我们求解表达式 \\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\) 的值。这类题目常见于代数基础部分,考查学生对代数式的基本运算和代入法的掌握。\\\\n\\\\n### 【方法点拨】:\\\\n1. **简化表达式**:首先对给定的表达式进行简化,合并同类项。\\\\n2. **代入已知条件**:将 \\\\\\\\(a + b = -1\\\\\\\\) 和 \\\\\\\\(ab = 4\\\\\\\\) 代入简化后的表达式中,进行计算。\\\\n3. **逐步求解**:通过逐步代入和计算,得到最终结果。\\\\n\\\\n### 【详细解析】:\\\\n\\\\n#### 第一步:简化表达式\\\\n表达式为 \\\\\\\\((4a - 5b - 3ab) - (3a - 6b + ab)\\\\\\\\)。\\\\n\\\\n先去掉括号并合并同类项:\\\\n\\\\\\\\[\\\\n(4a - 5b - 3ab) - (3a - 6b + ab) = 4a - 5b - 3ab - 3a + 6b - ab\\\\n\\\\\\\\]\\\\n\\\\n合并同类项:\\\\n\\\\\\\\[\\\\n= (4a - 3a) + (-5b + 6b) + (-3ab - ab) = a + b - 4ab\\\\n\\\\\\\\]\\\\n\\\\n#### 第二步:代入已知条件\\\\n根据题目条件 \\\\\\\\(a + b = -1\\\\\\\\) 和 \\\\\\\\(ab = 4\\\\\\\\),将这些值代入简化后的表达式:\\\\n\\\\\\\\[\\\\na + b - 4ab = -1 - 4 \\\\\\\\times 4 = -1 - 16 = -17\\\\n\\\\\\\\]\\\\n\\\\n#### 第三步:得出最终结果\\\\n因此,表达式的值为 \\\\\\\\(-17\\\\\\\\)。\\\\n\\\\n### 【最终答案】:\\\\n\\\\\\\\(\\\\\\\\boxed{-17}\\\\\\\\) \\\\n\\\\n所以,该表达式的值为 \\\\\\\\(\\\\\\\\boxed{-17}\\\\\\\\)。"'."\n"
.' }'."\n"
.' ],'."\n"
.' "role": "assistant"'."\n"
.' }'."\n"
.'}'."\n"
.'```',
],
],
'endpoints' => [
[
'regionId' => 'cn-hangzhou',
'endpoint' => 'edututor.cn-hangzhou.aliyuncs.com',
],
],
];
|