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Expression of type Equals

from the theory of proveit.linear_algebra.addition

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import v, w, x, y, z
from proveit.linear_algebra import TensorProd, VecAdd
from proveit.logic import Equals
In [2]:
# build up the expression from sub-expressions
expr = Equals(VecAdd(TensorProd(x, y, z), TensorProd(x, y, w), TensorProd(x, y, v)), VecAdd(TensorProd(x, TensorProd(y, z)), TensorProd(x, TensorProd(y, w)), TensorProd(x, TensorProd(y, v))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(x {\otimes} y {\otimes} z\right) + \left(x {\otimes} y {\otimes} w\right) + \left(x {\otimes} y {\otimes} v\right)\right) = \left(\left(x {\otimes} \left(y {\otimes} z\right)\right) + \left(x {\otimes} \left(y {\otimes} w\right)\right) + \left(x {\otimes} \left(y {\otimes} v\right)\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9, 10
6Literal
7ExprTuple11, 12, 13
8Operationoperator: 26
operands: 14
9Operationoperator: 26
operands: 15
10Operationoperator: 26
operands: 16
11Operationoperator: 26
operands: 17
12Operationoperator: 26
operands: 18
13Operationoperator: 26
operands: 19
14ExprTuple22, 30, 28
15ExprTuple22, 30, 29
16ExprTuple22, 30, 31
17ExprTuple22, 20
18ExprTuple22, 21
19ExprTuple22, 23
20Operationoperator: 26
operands: 24
21Operationoperator: 26
operands: 25
22Variable
23Operationoperator: 26
operands: 27
24ExprTuple30, 28
25ExprTuple30, 29
26Literal
27ExprTuple30, 31
28Variable
29Variable
30Variable
31Variable