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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, fi, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, Mult, four, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(gamma, beta)
sub_expr2 = VecSum(index_or_indices = [i], summand = fi, domain = Interval(two, four))
expr = Equals(TensorProd(x, ScalarMult(sub_expr1, sub_expr2), y), ScalarMult(sub_expr1, TensorProd(x, sub_expr2, y))).with_wrapping_at(1)
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())
\begin{array}{c} \begin{array}{l} \left(x {\otimes} \left(\left(\gamma \cdot \beta\right) \cdot \left(\sum_{i=2}^{4} f\left(i\right)\right)\right) {\otimes} y\right) \\  = \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} \left(\sum_{i=2}^{4} f\left(i\right)\right) {\otimes} y\right)\right) \end{array} \end{array}
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.()(1)('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: 11
operands: 5
4Operationoperator: 9
operands: 6
5ExprTuple14, 7, 16
6ExprTuple13, 8
7Operationoperator: 9
operands: 10
8Operationoperator: 11
operands: 12
9Literal
10ExprTuple13, 15
11Literal
12ExprTuple14, 15, 16
13Operationoperator: 17
operands: 18
14Variable
15Operationoperator: 19
operand: 23
16Variable
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple23
21Variable
22Variable
23Lambdaparameter: 31
body: 24
24Conditionalvalue: 25
condition: 26
25Operationoperator: 27
operand: 31
26Operationoperator: 29
operands: 30
27Variable
28ExprTuple31
29Literal
30ExprTuple31, 32
31Variable
32Operationoperator: 33
operands: 34
33Literal
34ExprTuple35, 36
35Literal
36Literal