logo

Expression of type Equals

from the theory of proveit.linear_algebra.tensors

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 beta, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = ScalarMult(beta, ScalarMult(Add(i, one), TensorProd(x, y)))
expr = Equals(ScalarMult(gamma, ScalarMult(i, sub_expr1)), ScalarMult(ScalarMult(gamma, i), sub_expr1))
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(\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right)\right) = \left(\left(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\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: 16
operands: 5
4Operationoperator: 16
operands: 6
5ExprTuple12, 7
6ExprTuple8, 11
7Operationoperator: 16
operands: 9
8Operationoperator: 16
operands: 10
9ExprTuple24, 11
10ExprTuple12, 24
11Operationoperator: 16
operands: 13
12Variable
13ExprTuple14, 15
14Variable
15Operationoperator: 16
operands: 17
16Literal
17ExprTuple18, 19
18Operationoperator: 20
operands: 21
19Operationoperator: 22
operands: 23
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple26, 27
24Variable
25Literal
26Variable
27Variable