[fix](index) Fix create index/index def to sql

fe/fe-core/src/main/java/org/apache/doris/alter/SchemaChangeHandler.java

@@ -1919,7 +1919,7 @@ public void process(String rawSql, List<AlterClause> alterClauses, Database db,
             // index id -> index schema
             Map<Long, LinkedList<Column>> indexSchemaMap = new HashMap<>();
 
-            //for multi add colmuns clauses
+            //for multi add columns clauses
             //index id -> index col_unique_id supplier
             Map<Long, IntSupplier> colUniqueIdSupplierMap = new HashMap<>();
             for (Map.Entry<Long, List<Column>> entry : olapTable.getIndexIdToSchema(true).entrySet()) {
@@ -2749,7 +2749,7 @@ private boolean processAddIndex(CreateIndexClause alterClause, OlapTable olapTab
         // the column name in CreateIndexClause is not check case sensitivity,
         // when send index description to BE, there maybe cannot find column by name,
         // so here update column name in CreateIndexClause after checkColumn for indexDef,
-        // there will use the column name in olapTable insead of the column name in CreateIndexClause.
+        // there will use the column name in olapTable instead of the column name in CreateIndexClause.
         alterIndex.setColumns(indexDef.getColumns());
         alterIndex.setColumnUniqueIds(indexDef.getColumnUniqueIds());
         newIndexes.add(alterIndex);

fe/fe-core/src/main/java/org/apache/doris/analysis/CreateIndexClause.java

@@ -89,7 +89,7 @@ public boolean needChangeMTMVState() {
     @Override
     public String toSql() {
         if (alter) {
-            return indexDef.toSql();
+            return "ADD " + indexDef.toSql();
         } else {
             return "CREATE " + indexDef.toSql(tableName.toSql());
         }

fe/fe-core/src/main/java/org/apache/doris/analysis/IndexDef.java

@@ -118,7 +118,7 @@ public String toSql() {
 
     public String toSql(String tableName) {
         StringBuilder sb = new StringBuilder("INDEX ");
-        sb.append(indexName);
+        sb.append("`" + indexName + "`");
         if (tableName != null && !tableName.isEmpty()) {
             sb.append(" ON ").append(tableName);
         }

fe/fe-core/src/main/java/org/apache/doris/catalog/Index.java

@@ -54,7 +54,7 @@ public class Index implements Writable {
     public static final int INDEX_ID_INIT_VALUE = -1;
 
     @SerializedName(value = "i", alternate = {"indexId"})
-    private long indexId = -1; // -1 for compatibale
+    private long indexId = -1; // -1 for compatiable
     @SerializedName(value = "in", alternate = {"indexName"})
     private String indexName;
     @SerializedName(value = "c", alternate = {"columns"})

fe/fe-core/src/test/java/org/apache/doris/analysis/CreateIndexClauseTest.java

@@ -40,11 +40,22 @@ public void testNormal() throws AnalysisException {
                 new IndexDef("index1", false, Lists.newArrayList("col1"), IndexDef.IndexType.INVERTED, null, "balabala"),
                 false);
         clause.analyze(analyzer);
-        Assert.assertEquals("CREATE INDEX index1 ON `db`.`table` (`col1`) USING INVERTED COMMENT 'balabala'",
+        Assert.assertEquals("CREATE INDEX `index1` ON `db`.`table` (`col1`) USING INVERTED COMMENT 'balabala'",
                 clause.toSql());
 
     }
 
+    @Test
+    public void testAlter() throws AnalysisException {
+        CreateIndexClause clause = new CreateIndexClause(
+                new TableName(InternalCatalog.INTERNAL_CATALOG_NAME, "db", "table"),
+                new IndexDef("index1", false, Lists.newArrayList("col1"), IndexDef.IndexType.INVERTED, null, "balabala"),
+                true);
+        clause.analyze(analyzer);
+        Assert.assertEquals("ALTER TABLE `db`.`table` ADD INDEX `index1` (`col1`) USING INVERTED COMMENT 'balabala'",
+                clause.toSql());
+    }
+
     @Test(expected = AnalysisException.class)
     public void testDuplIndex() throws AnalysisException {
         CreateIndexClause clause = new CreateIndexClause(

fe/fe-core/src/test/java/org/apache/doris/analysis/DropIndexClauseTest.java

@@ -39,7 +39,15 @@ public void testNormal() throws UserException {
         DropIndexClause clause = new DropIndexClause("index1", false,
                 new TableName(InternalCatalog.INTERNAL_CATALOG_NAME, "db", "table"), false);
         clause.analyze(analyzer);
-        Assert.assertEquals("DROP INDEX index1 ON `db`.`table`", clause.toSql());
+        Assert.assertEquals("DROP INDEX `index1` ON `db`.`table`", clause.toSql());
+    }
+
+    @Test
+    public void testAlter() throws UserException {
+        DropIndexClause clause = new DropIndexClause("index1", false,
+                new TableName(InternalCatalog.INTERNAL_CATALOG_NAME, "db", "table"), true);
+        clause.analyze(analyzer);
+        Assert.assertEquals("ALTER TABLE `db`.`table` DROP INDEX `index1`", clause.toSql());
     }
 
     @Test(expected = AnalysisException.class)

fe/fe-core/src/test/java/org/apache/doris/analysis/IndexDefTest.java

@@ -77,8 +77,8 @@ public void testAnalyzeExpection() throws AnalysisException {
 
     @Test
     public void toSql() {
-        Assert.assertEquals("INDEX index1 (`col1`) USING INVERTED COMMENT 'balabala'", def.toSql());
-        Assert.assertEquals("INDEX index1 ON table1 (`col1`) USING INVERTED COMMENT 'balabala'",
+        Assert.assertEquals("INDEX `index1` (`col1`) USING INVERTED COMMENT 'balabala'", def.toSql());
+        Assert.assertEquals("INDEX `index1` ON table1 (`col1`) USING INVERTED COMMENT 'balabala'",
                 def.toSql("table1"));
     }
 }